James D. McCaffrey

The RANSAC (random sample consensus) regression technique can be used when the training dataset is known to have outliers (typically, blatant errors). RANSAC is a meta-heuristic that can be applied to any base regression technique, but is usually applied to basic linear regression.

The idea is:

inliers = []
loop many times
  take a very small sample from train data
  train a model
  use model on train data to find inliers
  if enough inliers
    train a "good" model on inliers
  end-if
end-loop
return best model found

I usually think of RANSAC as a kind of automatic outlier detection and removal, combined with regression. Before I go any further, let me note that the original RANSAC idea was developed in 1980 for a very specific image processing problem scenario, and the idea works quite well. But RANSAC has been applied to more general regression scenarios, and I am not a fan of RANSAC in those general scenarios.

I put together a RANSAC regression demo using the scikit-learn RANSACRegressor module on the Diabetes Dataset. The output of the demo:

Begin scikit RANSAC (random sample consensus)
 on Diabetes Dataset demo

Loading diabetes train (342), test (100) data
Done

First three X predictors:
[0.5900 1.0000 0.3210 0.1010 0.1570 0.0932 0.3800 0.4000
 0.4860 0.0870]
[0.4800 0.0000 0.2160 0.0870 0.1830 0.1032 0.7000 0.3000
 0.3892 0.0690]
[0.7200 1.0000 0.3050 0.0930 0.1560 0.0936 0.4100 0.4000
 0.4673 0.0850]

First three y targets:
0.1510
0.0750
0.1410

Creating scikit RANSAC model
Done

Training RANSAC model
Done.

Evaluating model

Accuracy (within 0.10) train = 0.1462
Accuracy (within 0.10) test = 0.1413

MSE train = 0.0040
MSE test = 0.0049

===============================

Creating, training base linear regression model

LR accuracy (within 0.10) train = 0.1813
LR accuracy (within 0.10) test = 0.2500

LR MSE train = 0.0029
LR MSE test = 0.0028

End demo

The RANSAC results were poor, as expected, and the RANSAC results were even worse than just plain linear regression, as expected.

The raw Diabetes Dataset looks like:

59, 2, 32.1, 101.00, 157,  93.2, 38, 4.00, 4.8598, 87, 151
48, 1, 21.6,  87.00, 183, 103.2, 70, 3.00, 3.8918, 69,  75
72, 2, 30.5,  93.00, 156,  93.6, 41, 4.00, 4.6728, 85, 141
. . .

Each line represents a patient. The first 10 values on each line are predictors. The last value on each line is the target value (a diabetes metric) to predict. The predictors are: age, sex, body mass index, blood pressure, serum cholesterol, low-density lipoproteins, high-density lipoproteins, total cholesterol, triglycerides, blood sugar. There are 442 data items.

The sex encoding isn’t explained anywhere but I suspect male = 1, female = 2 because there are 235 1 values and 206 2 values).

Note that this Diabetes Dataset, which is included as an example dataset in the Python language scikit-learn library, is not the same as the Pima Diabetes Dataset from the UCI dataset repository. See https://jamesmccaffreyblog.com/2026/02/03/the-origin-and-history-of-scikit-learn-diabetes-dataset/.

I tracked down, and read, the original 1980 RANSAC paper.

I converted the sex values from 1,2 into 0,1. Then I applied divide-by-constant normalization by dividing the 10 predictor columns by (100, 1, 100, 1000, 1000, 1000, 100, 10, 10, 1000) and the target y values by 1000. The resulting encoded and normalized data looks like:

0.5900, 1.0000, 0.3210, . . . 0.1510
0.4800, 0.0000, 0.2160, . . . 0.0750
0.7200, 1.0000, 0.3050, . . . 0.1410
. . .

I split the 442-items into a 342-item training set and a 100-item test set. I have done many experiments with the Diabetes Dataset and I’ve concluded the the default target value in the last column (a patient diabetes score) simply cannot be predicted well. But the variables in columns [4], [5], [6], [7], and [8] can be meaningfully predicted from the other columns.

In some sense, machine learning regression can be thought of as searching for hidden patterns in data.

Left: On the cover of the issue from February 1993, the bunny logo is very difficult to spot. It’s incorporated into the long red threads on the model’s clothing. I added a white circle for you. Right: One of the most difficult hidden logos ever: on the cover of the July 1993 issue, the bunny logo is disguised as part of the water reflections. I circled it in red for you.

Demo program. Replace “lt” (less than) in the accuracy() function with the Boolean less-than operator symbol. (My blog editor chokes on symbols).

# diabetes_scikit_ransac.py
# RANSAC (random sample consensus)
# for the Diabetes Dataset

import numpy as np
from sklearn.linear_model import RANSACRegressor

# RANSACRegressor(estimator=None, *, min_samples=None,
# residual_threshold=None, is_data_valid=None,
# is_model_valid=None, max_trials=100, max_skips=inf,
# stop_n_inliers=inf, stop_score=inf,
# stop_probability=0.99, loss='absolute_error',
# random_state=None)

# -----------------------------------------------------------

np.set_printoptions(precision=4, suppress=True,
  floatmode='fixed', linewidth=60)

# -----------------------------------------------------------

def accuracy(model, data_X, data_y, pct_close):
  n = len(data_X)
  n_correct = 0; n_wrong = 0
  for i in range(n):
    x = data_X[i].reshape(1,-1)
    y = data_y[i]
    y_pred = model.predict(x)[0]

    if np.abs(y - y_pred) "lt" np.abs(y * pct_close):
      n_correct += 1
    else: 
      n_wrong += 1
  return n_correct / (n_correct + n_wrong)

def mse(model, data_X, data_y):
  n = len(data_X)
  sum = 0.0
  for i in range(n):
    actual_y = data_y[i]
    pred_y = model.predict(data_X[i].reshape(1, -1))[0]
    diff = actual_y - pred_y
    sum += diff * diff
  return sum /n

# -----------------------------------------------------------

print("\nBegin scikit RANSAC (random sample consensus) " +\
 "on Diabetes Dataset demo ")

print("\nLoading diabetes train (342), test (100) data ")
train_file = ".\\Data\\diabetes_norm_train_342.txt"

cols_X = [0,1,2,3,4,5,6,7,8,9]  
col_y = 10  # cols # 4 5 6 7 8 are much better
train_X = np.loadtxt(train_file, comments="#",
  usecols=cols_X, delimiter=",",  dtype=np.float64)
train_y = np.loadtxt(train_file, comments="#",
  usecols=col_y, delimiter=",",  dtype=np.float64)

test_file = ".\\Data\\diabetes_norm_test_100.txt"
test_X = np.loadtxt(test_file, comments="#",
  usecols=cols_X, delimiter=",",  dtype=np.float64)
test_y = np.loadtxt(test_file, comments="#",
  usecols=col_y, delimiter=",",  dtype=np.float64)
print("Done ")

# alternative normalization and split
# from sklearn.datasets import load_diabetes
# from sklearn.model_selection import train_test_split
# X, y = load_diabetes(return_X_y=True, scaled=True)
# train_X, test_X, train_y, test_y = \
#   train_test_split(X, y, random_state=0)  # 25% test

print("\nFirst three X predictors: ")
for i in range(3):
  print(train_X[i])
print("\nFirst three y targets: ")
for i in range(3):
  print("%0.4f" % train_y[i])

print("\nCreating scikit RANSAC model ")
model = RANSACRegressor(random_state=0)
print("Done ")

print("\nTraining RANSAC model ")
model.fit(train_X, train_y)
print("Done. ")

print("\nEvaluating model ")
acc_train = accuracy(model, train_X, train_y, 0.10)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
print("Accuracy (within 0.10) test = %0.4f " % \
  acc_test)

mse_train = mse(model, train_X, train_y)
mse_test = mse(model, test_X, test_y)
print("\nMSE train = %0.4f " % mse_train)
print("MSE test = %0.4f " % mse_test)

print("\n=============================== ")

print("\nCreating, training base linear regression model")
from sklearn.linear_model import LinearRegression
lr_model = LinearRegression()
lr_model.fit(train_X, train_y)

acc_train = accuracy(lr_model, train_X, train_y, 0.10)
acc_test = accuracy(lr_model, test_X, test_y, 0.10)
print("\nLR accuracy (within 0.10) train = %0.4f " % \
  acc_train)
print("LR accuracy (within 0.10) test = %0.4f " % \
  acc_test)

mse_train = mse(lr_model, train_X, train_y)
mse_test = mse(lr_model, test_X, test_y)
print("\nLR MSE train = %0.4f " % mse_train)
print("LR MSE test = %0.4f " % mse_test)

print("\nEnd demo ")

Training data:

# diabetes_norm_train_342.txt
# cols [0] to [9] predictors. col [10] target
# norm division constants:
# 100, -1, 100, 1000, 1000, 1000, 100, 10, 10, 1000, 1000
#
0.5900, 1.0000, 0.3210, 0.1010, 0.1570, 0.0932, 0.3800, 0.4000, 0.4860, 0.0870, 0.1510
0.4800, 0.0000, 0.2160, 0.0870, 0.1830, 0.1032, 0.7000, 0.3000, 0.3892, 0.0690, 0.0750
0.7200, 1.0000, 0.3050, 0.0930, 0.1560, 0.0936, 0.4100, 0.4000, 0.4673, 0.0850, 0.1410
0.2400, 0.0000, 0.2530, 0.0840, 0.1980, 0.1314, 0.4000, 0.5000, 0.4890, 0.0890, 0.2060
0.5000, 0.0000, 0.2300, 0.1010, 0.1920, 0.1254, 0.5200, 0.4000, 0.4291, 0.0800, 0.1350
0.2300, 0.0000, 0.2260, 0.0890, 0.1390, 0.0648, 0.6100, 0.2000, 0.4190, 0.0680, 0.0970
0.3600, 1.0000, 0.2200, 0.0900, 0.1600, 0.0996, 0.5000, 0.3000, 0.3951, 0.0820, 0.1380
0.6600, 1.0000, 0.2620, 0.1140, 0.2550, 0.1850, 0.5600, 0.4550, 0.4249, 0.0920, 0.0630
0.6000, 1.0000, 0.3210, 0.0830, 0.1790, 0.1194, 0.4200, 0.4000, 0.4477, 0.0940, 0.1100
0.2900, 0.0000, 0.3000, 0.0850, 0.1800, 0.0934, 0.4300, 0.4000, 0.5385, 0.0880, 0.3100
0.2200, 0.0000, 0.1860, 0.0970, 0.1140, 0.0576, 0.4600, 0.2000, 0.3951, 0.0830, 0.1010
0.5600, 1.0000, 0.2800, 0.0850, 0.1840, 0.1448, 0.3200, 0.6000, 0.3584, 0.0770, 0.0690
0.5300, 0.0000, 0.2370, 0.0920, 0.1860, 0.1092, 0.6200, 0.3000, 0.4304, 0.0810, 0.1790
0.5000, 1.0000, 0.2620, 0.0970, 0.1860, 0.1054, 0.4900, 0.4000, 0.5063, 0.0880, 0.1850
0.6100, 0.0000, 0.2400, 0.0910, 0.2020, 0.1154, 0.7200, 0.3000, 0.4291, 0.0730, 0.1180
0.3400, 1.0000, 0.2470, 0.1180, 0.2540, 0.1842, 0.3900, 0.7000, 0.5037, 0.0810, 0.1710
0.4700, 0.0000, 0.3030, 0.1090, 0.2070, 0.1002, 0.7000, 0.3000, 0.5215, 0.0980, 0.1660
0.6800, 1.0000, 0.2750, 0.1110, 0.2140, 0.1470, 0.3900, 0.5000, 0.4942, 0.0910, 0.1440
0.3800, 0.0000, 0.2540, 0.0840, 0.1620, 0.1030, 0.4200, 0.4000, 0.4443, 0.0870, 0.0970
0.4100, 0.0000, 0.2470, 0.0830, 0.1870, 0.1082, 0.6000, 0.3000, 0.4543, 0.0780, 0.1680
0.3500, 0.0000, 0.2110, 0.0820, 0.1560, 0.0878, 0.5000, 0.3000, 0.4511, 0.0950, 0.0680
0.2500, 1.0000, 0.2430, 0.0950, 0.1620, 0.0986, 0.5400, 0.3000, 0.3850, 0.0870, 0.0490
0.2500, 0.0000, 0.2600, 0.0920, 0.1870, 0.1204, 0.5600, 0.3000, 0.3970, 0.0880, 0.0680
0.6100, 1.0000, 0.3200, 0.1037, 0.2100, 0.0852, 0.3500, 0.6000, 0.6107, 0.1240, 0.2450
0.3100, 0.0000, 0.2970, 0.0880, 0.1670, 0.1034, 0.4800, 0.4000, 0.4357, 0.0780, 0.1840
0.3000, 1.0000, 0.2520, 0.0830, 0.1780, 0.1184, 0.3400, 0.5000, 0.4852, 0.0830, 0.2020
0.1900, 0.0000, 0.1920, 0.0870, 0.1240, 0.0540, 0.5700, 0.2000, 0.4174, 0.0900, 0.1370
0.4200, 0.0000, 0.3190, 0.0830, 0.1580, 0.0876, 0.5300, 0.3000, 0.4466, 0.1010, 0.0850
0.6300, 0.0000, 0.2440, 0.0730, 0.1600, 0.0914, 0.4800, 0.3000, 0.4635, 0.0780, 0.1310
0.6700, 1.0000, 0.2580, 0.1130, 0.1580, 0.0542, 0.6400, 0.2000, 0.5293, 0.1040, 0.2830
0.3200, 0.0000, 0.3050, 0.0890, 0.1820, 0.1106, 0.5600, 0.3000, 0.4344, 0.0890, 0.1290
0.4200, 0.0000, 0.2030, 0.0710, 0.1610, 0.0812, 0.6600, 0.2000, 0.4234, 0.0810, 0.0590
0.5800, 1.0000, 0.3800, 0.1030, 0.1500, 0.1072, 0.2200, 0.7000, 0.4644, 0.0980, 0.3410
0.5700, 0.0000, 0.2170, 0.0940, 0.1570, 0.0580, 0.8200, 0.2000, 0.4443, 0.0920, 0.0870
0.5300, 0.0000, 0.2050, 0.0780, 0.1470, 0.0842, 0.5200, 0.3000, 0.3989, 0.0750, 0.0650
0.6200, 1.0000, 0.2350, 0.0803, 0.2250, 0.1128, 0.8600, 0.2620, 0.4875, 0.0960, 0.1020
0.5200, 0.0000, 0.2850, 0.1100, 0.1950, 0.0972, 0.6000, 0.3000, 0.5242, 0.0850, 0.2650
0.4600, 0.0000, 0.2740, 0.0780, 0.1710, 0.0880, 0.5800, 0.3000, 0.4828, 0.0900, 0.2760
0.4800, 1.0000, 0.3300, 0.1230, 0.2530, 0.1636, 0.4400, 0.6000, 0.5425, 0.0970, 0.2520
0.4800, 1.0000, 0.2770, 0.0730, 0.1910, 0.1194, 0.4600, 0.4000, 0.4852, 0.0920, 0.0900
0.5000, 1.0000, 0.2560, 0.1010, 0.2290, 0.1622, 0.4300, 0.5000, 0.4779, 0.1140, 0.1000
0.2100, 0.0000, 0.2010, 0.0630, 0.1350, 0.0690, 0.5400, 0.3000, 0.4094, 0.0890, 0.0550
0.3200, 1.0000, 0.2540, 0.0903, 0.1530, 0.1004, 0.3400, 0.4500, 0.4533, 0.0830, 0.0610
0.5400, 0.0000, 0.2420, 0.0740, 0.2040, 0.1090, 0.8200, 0.2000, 0.4174, 0.1090, 0.0920
0.6100, 1.0000, 0.3270, 0.0970, 0.1770, 0.1184, 0.2900, 0.6000, 0.4997, 0.0870, 0.2590
0.5600, 1.0000, 0.2310, 0.1040, 0.1810, 0.1164, 0.4700, 0.4000, 0.4477, 0.0790, 0.0530
0.3300, 0.0000, 0.2530, 0.0850, 0.1550, 0.0850, 0.5100, 0.3000, 0.4554, 0.0700, 0.1900
0.2700, 0.0000, 0.1960, 0.0780, 0.1280, 0.0680, 0.4300, 0.3000, 0.4443, 0.0710, 0.1420
0.6700, 1.0000, 0.2250, 0.0980, 0.1910, 0.1192, 0.6100, 0.3000, 0.3989, 0.0860, 0.0750
0.3700, 1.0000, 0.2770, 0.0930, 0.1800, 0.1194, 0.3000, 0.6000, 0.5030, 0.0880, 0.1420
0.5800, 0.0000, 0.2570, 0.0990, 0.1570, 0.0916, 0.4900, 0.3000, 0.4407, 0.0930, 0.1550
0.6500, 1.0000, 0.2790, 0.1030, 0.1590, 0.0968, 0.4200, 0.4000, 0.4615, 0.0860, 0.2250
0.3400, 0.0000, 0.2550, 0.0930, 0.2180, 0.1440, 0.5700, 0.4000, 0.4443, 0.0880, 0.0590
0.4600, 0.0000, 0.2490, 0.1150, 0.1980, 0.1296, 0.5400, 0.4000, 0.4277, 0.1030, 0.1040
0.3500, 0.0000, 0.2870, 0.0970, 0.2040, 0.1268, 0.6400, 0.3000, 0.4190, 0.0930, 0.1820
0.3700, 0.0000, 0.2180, 0.0840, 0.1840, 0.1010, 0.7300, 0.3000, 0.3912, 0.0930, 0.1280
0.3700, 0.0000, 0.3020, 0.0870, 0.1660, 0.0960, 0.4000, 0.4150, 0.5011, 0.0870, 0.0520
0.4100, 0.0000, 0.2050, 0.0800, 0.1240, 0.0488, 0.6400, 0.2000, 0.4025, 0.0750, 0.0370
0.6000, 0.0000, 0.2040, 0.1050, 0.1980, 0.0784, 0.9900, 0.2000, 0.4635, 0.0790, 0.1700
0.6600, 1.0000, 0.2400, 0.0980, 0.2360, 0.1464, 0.5800, 0.4000, 0.5063, 0.0960, 0.1700
0.2900, 0.0000, 0.2600, 0.0830, 0.1410, 0.0652, 0.6400, 0.2000, 0.4078, 0.0830, 0.0610
0.3700, 1.0000, 0.2680, 0.0790, 0.1570, 0.0980, 0.2800, 0.6000, 0.5043, 0.0960, 0.1440
0.4100, 1.0000, 0.2570, 0.0830, 0.1810, 0.1066, 0.6600, 0.3000, 0.3738, 0.0850, 0.0520
0.3900, 0.0000, 0.2290, 0.0770, 0.2040, 0.1432, 0.4600, 0.4000, 0.4304, 0.0740, 0.1280
0.6700, 1.0000, 0.2400, 0.0830, 0.1430, 0.0772, 0.4900, 0.3000, 0.4431, 0.0940, 0.0710
0.3600, 1.0000, 0.2410, 0.1120, 0.1930, 0.1250, 0.3500, 0.6000, 0.5106, 0.0950, 0.1630
0.4600, 1.0000, 0.2470, 0.0850, 0.1740, 0.1232, 0.3000, 0.6000, 0.4644, 0.0960, 0.1500
0.6000, 1.0000, 0.2500, 0.0897, 0.1850, 0.1208, 0.4600, 0.4020, 0.4511, 0.0920, 0.0970
0.5900, 1.0000, 0.2360, 0.0830, 0.1650, 0.1000, 0.4700, 0.4000, 0.4500, 0.0920, 0.1600
0.5300, 0.0000, 0.2210, 0.0930, 0.1340, 0.0762, 0.4600, 0.3000, 0.4078, 0.0960, 0.1780
0.4800, 0.0000, 0.1990, 0.0910, 0.1890, 0.1096, 0.6900, 0.3000, 0.3951, 0.1010, 0.0480
0.4800, 0.0000, 0.2950, 0.1310, 0.2070, 0.1322, 0.4700, 0.4000, 0.4935, 0.1060, 0.2700
0.6600, 1.0000, 0.2600, 0.0910, 0.2640, 0.1466, 0.6500, 0.4000, 0.5568, 0.0870, 0.2020
0.5200, 1.0000, 0.2450, 0.0940, 0.2170, 0.1494, 0.4800, 0.5000, 0.4585, 0.0890, 0.1110
0.5200, 1.0000, 0.2660, 0.1110, 0.2090, 0.1264, 0.6100, 0.3000, 0.4682, 0.1090, 0.0850
0.4600, 1.0000, 0.2350, 0.0870, 0.1810, 0.1148, 0.4400, 0.4000, 0.4710, 0.0980, 0.0420
0.4000, 1.0000, 0.2900, 0.1150, 0.0970, 0.0472, 0.3500, 0.2770, 0.4304, 0.0950, 0.1700
0.2200, 0.0000, 0.2300, 0.0730, 0.1610, 0.0978, 0.5400, 0.3000, 0.3829, 0.0910, 0.2000
0.5000, 0.0000, 0.2100, 0.0880, 0.1400, 0.0718, 0.3500, 0.4000, 0.5112, 0.0710, 0.2520
0.2000, 0.0000, 0.2290, 0.0870, 0.1910, 0.1282, 0.5300, 0.4000, 0.3892, 0.0850, 0.1130
0.6800, 0.0000, 0.2750, 0.1070, 0.2410, 0.1496, 0.6400, 0.4000, 0.4920, 0.0900, 0.1430
0.5200, 1.0000, 0.2430, 0.0860, 0.1970, 0.1336, 0.4400, 0.5000, 0.4575, 0.0910, 0.0510
0.4400, 0.0000, 0.2310, 0.0870, 0.2130, 0.1264, 0.7700, 0.3000, 0.3871, 0.0720, 0.0520
0.3800, 0.0000, 0.2730, 0.0810, 0.1460, 0.0816, 0.4700, 0.3000, 0.4466, 0.0810, 0.2100
0.4900, 0.0000, 0.2270, 0.0653, 0.1680, 0.0962, 0.6200, 0.2710, 0.3892, 0.0600, 0.0650
0.6100, 0.0000, 0.3300, 0.0950, 0.1820, 0.1148, 0.5400, 0.3000, 0.4190, 0.0740, 0.1410
0.2900, 1.0000, 0.1940, 0.0830, 0.1520, 0.1058, 0.3900, 0.4000, 0.3584, 0.0830, 0.0550
0.6100, 0.0000, 0.2580, 0.0980, 0.2350, 0.1258, 0.7600, 0.3000, 0.5112, 0.0820, 0.1340
0.3400, 1.0000, 0.2260, 0.0750, 0.1660, 0.0918, 0.6000, 0.3000, 0.4263, 0.1080, 0.0420
0.3600, 0.0000, 0.2190, 0.0890, 0.1890, 0.1052, 0.6800, 0.3000, 0.4369, 0.0960, 0.1110
0.5200, 0.0000, 0.2400, 0.0830, 0.1670, 0.0866, 0.7100, 0.2000, 0.3850, 0.0940, 0.0980
0.6100, 0.0000, 0.3120, 0.0790, 0.2350, 0.1568, 0.4700, 0.5000, 0.5050, 0.0960, 0.1640
0.4300, 0.0000, 0.2680, 0.1230, 0.1930, 0.1022, 0.6700, 0.3000, 0.4779, 0.0940, 0.0480
0.3500, 0.0000, 0.2040, 0.0650, 0.1870, 0.1056, 0.6700, 0.2790, 0.4277, 0.0780, 0.0960
0.2700, 0.0000, 0.2480, 0.0910, 0.1890, 0.1068, 0.6900, 0.3000, 0.4190, 0.0690, 0.0900
0.2900, 0.0000, 0.2100, 0.0710, 0.1560, 0.0970, 0.3800, 0.4000, 0.4654, 0.0900, 0.1620
0.6400, 1.0000, 0.2730, 0.1090, 0.1860, 0.1076, 0.3800, 0.5000, 0.5308, 0.0990, 0.1500
0.4100, 0.0000, 0.3460, 0.0873, 0.2050, 0.1426, 0.4100, 0.5000, 0.4673, 0.1100, 0.2790
0.4900, 1.0000, 0.2590, 0.0910, 0.1780, 0.1066, 0.5200, 0.3000, 0.4575, 0.0750, 0.0920
0.4800, 0.0000, 0.2040, 0.0980, 0.2090, 0.1394, 0.4600, 0.5000, 0.4771, 0.0780, 0.0830
0.5300, 0.0000, 0.2800, 0.0880, 0.2330, 0.1438, 0.5800, 0.4000, 0.5050, 0.0910, 0.1280
0.5300, 1.0000, 0.2220, 0.1130, 0.1970, 0.1152, 0.6700, 0.3000, 0.4304, 0.1000, 0.1020
0.2300, 0.0000, 0.2900, 0.0900, 0.2160, 0.1314, 0.6500, 0.3000, 0.4585, 0.0910, 0.3020
0.6500, 1.0000, 0.3020, 0.0980, 0.2190, 0.1606, 0.4000, 0.5000, 0.4522, 0.0840, 0.1980
0.4100, 0.0000, 0.3240, 0.0940, 0.1710, 0.1044, 0.5600, 0.3000, 0.3970, 0.0760, 0.0950
0.5500, 1.0000, 0.2340, 0.0830, 0.1660, 0.1016, 0.4600, 0.4000, 0.4522, 0.0960, 0.0530
0.2200, 0.0000, 0.1930, 0.0820, 0.1560, 0.0932, 0.5200, 0.3000, 0.3989, 0.0710, 0.1340
0.5600, 0.0000, 0.3100, 0.0787, 0.1870, 0.1414, 0.3400, 0.5500, 0.4060, 0.0900, 0.1440
0.5400, 1.0000, 0.3060, 0.1033, 0.1440, 0.0798, 0.3000, 0.4800, 0.5142, 0.1010, 0.2320
0.5900, 1.0000, 0.2550, 0.0953, 0.1900, 0.1394, 0.3500, 0.5430, 0.4357, 0.1170, 0.0810
0.6000, 1.0000, 0.2340, 0.0880, 0.1530, 0.0898, 0.5800, 0.3000, 0.3258, 0.0950, 0.1040
0.5400, 0.0000, 0.2680, 0.0870, 0.2060, 0.1220, 0.6800, 0.3000, 0.4382, 0.0800, 0.0590
0.2500, 0.0000, 0.2830, 0.0870, 0.1930, 0.1280, 0.4900, 0.4000, 0.4382, 0.0920, 0.2460
0.5400, 1.0000, 0.2770, 0.1130, 0.2000, 0.1284, 0.3700, 0.5000, 0.5153, 0.1130, 0.2970
0.5500, 0.0000, 0.3660, 0.1130, 0.1990, 0.0944, 0.4300, 0.4630, 0.5730, 0.0970, 0.2580
0.4000, 1.0000, 0.2650, 0.0930, 0.2360, 0.1470, 0.3700, 0.7000, 0.5561, 0.0920, 0.2290
0.6200, 1.0000, 0.3180, 0.1150, 0.1990, 0.1286, 0.4400, 0.5000, 0.4883, 0.0980, 0.2750
0.6500, 0.0000, 0.2440, 0.1200, 0.2220, 0.1356, 0.3700, 0.6000, 0.5509, 0.1240, 0.2810
0.3300, 1.0000, 0.2540, 0.1020, 0.2060, 0.1410, 0.3900, 0.5000, 0.4868, 0.1050, 0.1790
0.5300, 0.0000, 0.2200, 0.0940, 0.1750, 0.0880, 0.5900, 0.3000, 0.4942, 0.0980, 0.2000
0.3500, 0.0000, 0.2680, 0.0980, 0.1620, 0.1036, 0.4500, 0.4000, 0.4205, 0.0860, 0.2000
0.6600, 0.0000, 0.2800, 0.1010, 0.1950, 0.1292, 0.4000, 0.5000, 0.4860, 0.0940, 0.1730
0.6200, 1.0000, 0.3390, 0.1010, 0.2210, 0.1564, 0.3500, 0.6000, 0.4997, 0.1030, 0.1800
0.5000, 1.0000, 0.2960, 0.0943, 0.3000, 0.2424, 0.3300, 0.9090, 0.4812, 0.1090, 0.0840
0.4700, 0.0000, 0.2860, 0.0970, 0.1640, 0.0906, 0.5600, 0.3000, 0.4466, 0.0880, 0.1210
0.4700, 1.0000, 0.2560, 0.0940, 0.1650, 0.0748, 0.4000, 0.4000, 0.5526, 0.0930, 0.1610
0.2400, 0.0000, 0.2070, 0.0870, 0.1490, 0.0806, 0.6100, 0.2000, 0.3611, 0.0780, 0.0990
0.5800, 1.0000, 0.2620, 0.0910, 0.2170, 0.1242, 0.7100, 0.3000, 0.4691, 0.0680, 0.1090
0.3400, 0.0000, 0.2060, 0.0870, 0.1850, 0.1122, 0.5800, 0.3000, 0.4304, 0.0740, 0.1150
0.5100, 0.0000, 0.2790, 0.0960, 0.1960, 0.1222, 0.4200, 0.5000, 0.5069, 0.1200, 0.2680
0.3100, 1.0000, 0.3530, 0.1250, 0.1870, 0.1124, 0.4800, 0.4000, 0.4890, 0.1090, 0.2740
0.2200, 0.0000, 0.1990, 0.0750, 0.1750, 0.1086, 0.5400, 0.3000, 0.4127, 0.0720, 0.1580
0.5300, 1.0000, 0.2440, 0.0920, 0.2140, 0.1460, 0.5000, 0.4000, 0.4500, 0.0970, 0.1070
0.3700, 1.0000, 0.2140, 0.0830, 0.1280, 0.0696, 0.4900, 0.3000, 0.3850, 0.0840, 0.0830
0.2800, 0.0000, 0.3040, 0.0850, 0.1980, 0.1156, 0.6700, 0.3000, 0.4344, 0.0800, 0.1030
0.4700, 0.0000, 0.3160, 0.0840, 0.1540, 0.0880, 0.3000, 0.5100, 0.5199, 0.1050, 0.2720
0.2300, 0.0000, 0.1880, 0.0780, 0.1450, 0.0720, 0.6300, 0.2000, 0.3912, 0.0860, 0.0850
0.5000, 0.0000, 0.3100, 0.1230, 0.1780, 0.1050, 0.4800, 0.4000, 0.4828, 0.0880, 0.2800
0.5800, 1.0000, 0.3670, 0.1170, 0.1660, 0.0938, 0.4400, 0.4000, 0.4949, 0.1090, 0.3360
0.5500, 0.0000, 0.3210, 0.1100, 0.1640, 0.0842, 0.4200, 0.4000, 0.5242, 0.0900, 0.2810
0.6000, 1.0000, 0.2770, 0.1070, 0.1670, 0.1146, 0.3800, 0.4000, 0.4277, 0.0950, 0.1180
0.4100, 0.0000, 0.3080, 0.0810, 0.2140, 0.1520, 0.2800, 0.7600, 0.5136, 0.1230, 0.3170
0.6000, 1.0000, 0.2750, 0.1060, 0.2290, 0.1438, 0.5100, 0.4000, 0.5142, 0.0910, 0.2350
0.4000, 0.0000, 0.2690, 0.0920, 0.2030, 0.1198, 0.7000, 0.3000, 0.4190, 0.0810, 0.0600
0.5700, 1.0000, 0.3070, 0.0900, 0.2040, 0.1478, 0.3400, 0.6000, 0.4710, 0.0930, 0.1740
0.3700, 0.0000, 0.3830, 0.1130, 0.1650, 0.0946, 0.5300, 0.3000, 0.4466, 0.0790, 0.2590
0.4000, 1.0000, 0.3190, 0.0950, 0.1980, 0.1356, 0.3800, 0.5000, 0.4804, 0.0930, 0.1780
0.3300, 0.0000, 0.3500, 0.0890, 0.2000, 0.1304, 0.4200, 0.4760, 0.4927, 0.1010, 0.1280
0.3200, 1.0000, 0.2780, 0.0890, 0.2160, 0.1462, 0.5500, 0.4000, 0.4304, 0.0910, 0.0960
0.3500, 1.0000, 0.2590, 0.0810, 0.1740, 0.1024, 0.3100, 0.6000, 0.5313, 0.0820, 0.1260
0.5500, 0.0000, 0.3290, 0.1020, 0.1640, 0.1062, 0.4100, 0.4000, 0.4431, 0.0890, 0.2880
0.4900, 0.0000, 0.2600, 0.0930, 0.1830, 0.1002, 0.6400, 0.3000, 0.4543, 0.0880, 0.0880
0.3900, 1.0000, 0.2630, 0.1150, 0.2180, 0.1582, 0.3200, 0.7000, 0.4935, 0.1090, 0.2920
0.6000, 1.0000, 0.2230, 0.1130, 0.1860, 0.1258, 0.4600, 0.4000, 0.4263, 0.0940, 0.0710
0.6700, 1.0000, 0.2830, 0.0930, 0.2040, 0.1322, 0.4900, 0.4000, 0.4736, 0.0920, 0.1970
0.4100, 1.0000, 0.3200, 0.1090, 0.2510, 0.1706, 0.4900, 0.5000, 0.5056, 0.1030, 0.1860
0.4400, 0.0000, 0.2540, 0.0950, 0.1620, 0.0926, 0.5300, 0.3000, 0.4407, 0.0830, 0.0250
0.4800, 1.0000, 0.2330, 0.0893, 0.2120, 0.1428, 0.4600, 0.4610, 0.4754, 0.0980, 0.0840
0.4500, 0.0000, 0.2030, 0.0743, 0.1900, 0.1262, 0.4900, 0.3880, 0.4304, 0.0790, 0.0960
0.4700, 0.0000, 0.3040, 0.1200, 0.1990, 0.1200, 0.4600, 0.4000, 0.5106, 0.0870, 0.1950
0.4600, 0.0000, 0.2060, 0.0730, 0.1720, 0.1070, 0.5100, 0.3000, 0.4249, 0.0800, 0.0530
0.3600, 1.0000, 0.3230, 0.1150, 0.2860, 0.1994, 0.3900, 0.7000, 0.5472, 0.1120, 0.2170
0.3400, 0.0000, 0.2920, 0.0730, 0.1720, 0.1082, 0.4900, 0.4000, 0.4304, 0.0910, 0.1720
0.5300, 1.0000, 0.3310, 0.1170, 0.1830, 0.1190, 0.4800, 0.4000, 0.4382, 0.1060, 0.1310
0.6100, 0.0000, 0.2460, 0.1010, 0.2090, 0.1068, 0.7700, 0.3000, 0.4836, 0.0880, 0.2140
0.3700, 0.0000, 0.2020, 0.0810, 0.1620, 0.0878, 0.6300, 0.3000, 0.4025, 0.0880, 0.0590
0.3300, 1.0000, 0.2080, 0.0840, 0.1250, 0.0702, 0.4600, 0.3000, 0.3784, 0.0660, 0.0700
0.6800, 0.0000, 0.3280, 0.1057, 0.2050, 0.1164, 0.4000, 0.5130, 0.5493, 0.1170, 0.2200
0.4900, 1.0000, 0.3190, 0.0940, 0.2340, 0.1558, 0.3400, 0.7000, 0.5398, 0.1220, 0.2680
0.4800, 0.0000, 0.2390, 0.1090, 0.2320, 0.1052, 0.3700, 0.6000, 0.6107, 0.0960, 0.1520
0.5500, 1.0000, 0.2450, 0.0840, 0.1790, 0.1058, 0.6600, 0.3000, 0.3584, 0.0870, 0.0470
0.4300, 0.0000, 0.2210, 0.0660, 0.1340, 0.0772, 0.4500, 0.3000, 0.4078, 0.0800, 0.0740
0.6000, 1.0000, 0.3300, 0.0970, 0.2170, 0.1256, 0.4500, 0.5000, 0.5447, 0.1120, 0.2950
0.3100, 1.0000, 0.1900, 0.0930, 0.1370, 0.0730, 0.4700, 0.3000, 0.4443, 0.0780, 0.1010
0.5300, 1.0000, 0.2730, 0.0820, 0.1190, 0.0550, 0.3900, 0.3000, 0.4828, 0.0930, 0.1510
0.6700, 0.0000, 0.2280, 0.0870, 0.1660, 0.0986, 0.5200, 0.3000, 0.4344, 0.0920, 0.1270
0.6100, 1.0000, 0.2820, 0.1060, 0.2040, 0.1320, 0.5200, 0.4000, 0.4605, 0.0960, 0.2370
0.6200, 0.0000, 0.2890, 0.0873, 0.2060, 0.1272, 0.3300, 0.6240, 0.5434, 0.0990, 0.2250
0.6000, 0.0000, 0.2560, 0.0870, 0.2070, 0.1258, 0.6900, 0.3000, 0.4111, 0.0840, 0.0810
0.4200, 0.0000, 0.2490, 0.0910, 0.2040, 0.1418, 0.3800, 0.5000, 0.4796, 0.0890, 0.1510
0.3800, 1.0000, 0.2680, 0.1050, 0.1810, 0.1192, 0.3700, 0.5000, 0.4820, 0.0910, 0.1070
0.6200, 0.0000, 0.2240, 0.0790, 0.2220, 0.1474, 0.5900, 0.4000, 0.4357, 0.0760, 0.0640
0.6100, 1.0000, 0.2690, 0.1110, 0.2360, 0.1724, 0.3900, 0.6000, 0.4812, 0.0890, 0.1380
0.6100, 1.0000, 0.2310, 0.1130, 0.1860, 0.1144, 0.4700, 0.4000, 0.4812, 0.1050, 0.1850
0.5300, 0.0000, 0.2860, 0.0880, 0.1710, 0.0988, 0.4100, 0.4000, 0.5050, 0.0990, 0.2650
0.2800, 1.0000, 0.2470, 0.0970, 0.1750, 0.0996, 0.3200, 0.5000, 0.5380, 0.0870, 0.1010
0.2600, 1.0000, 0.3030, 0.0890, 0.2180, 0.1522, 0.3100, 0.7000, 0.5159, 0.0820, 0.1370
0.3000, 0.0000, 0.2130, 0.0870, 0.1340, 0.0630, 0.6300, 0.2000, 0.3689, 0.0660, 0.1430
0.5000, 0.0000, 0.2610, 0.1090, 0.2430, 0.1606, 0.6200, 0.4000, 0.4625, 0.0890, 0.1410
0.4800, 0.0000, 0.2020, 0.0950, 0.1870, 0.1174, 0.5300, 0.4000, 0.4419, 0.0850, 0.0790
0.5100, 0.0000, 0.2520, 0.1030, 0.1760, 0.1122, 0.3700, 0.5000, 0.4898, 0.0900, 0.2920
0.4700, 1.0000, 0.2250, 0.0820, 0.1310, 0.0668, 0.4100, 0.3000, 0.4754, 0.0890, 0.1780
0.6400, 1.0000, 0.2350, 0.0970, 0.2030, 0.1290, 0.5900, 0.3000, 0.4318, 0.0770, 0.0910
0.5100, 1.0000, 0.2590, 0.0760, 0.2400, 0.1690, 0.3900, 0.6000, 0.5075, 0.0960, 0.1160
0.3000, 0.0000, 0.2090, 0.1040, 0.1520, 0.0838, 0.4700, 0.3000, 0.4663, 0.0970, 0.0860
0.5600, 1.0000, 0.2870, 0.0990, 0.2080, 0.1464, 0.3900, 0.5000, 0.4727, 0.0970, 0.1220
0.4200, 0.0000, 0.2210, 0.0850, 0.2130, 0.1386, 0.6000, 0.4000, 0.4277, 0.0940, 0.0720
0.6200, 1.0000, 0.2670, 0.1150, 0.1830, 0.1240, 0.3500, 0.5000, 0.4788, 0.1000, 0.1290
0.3400, 0.0000, 0.3140, 0.0870, 0.1490, 0.0938, 0.4600, 0.3000, 0.3829, 0.0770, 0.1420
0.6000, 0.0000, 0.2220, 0.1047, 0.2210, 0.1054, 0.6000, 0.3680, 0.5628, 0.0930, 0.0900
0.6400, 0.0000, 0.2100, 0.0923, 0.2270, 0.1468, 0.6500, 0.3490, 0.4331, 0.1020, 0.1580
0.3900, 1.0000, 0.2120, 0.0900, 0.1820, 0.1104, 0.6000, 0.3000, 0.4060, 0.0980, 0.0390
0.7100, 1.0000, 0.2650, 0.1050, 0.2810, 0.1736, 0.5500, 0.5000, 0.5568, 0.0840, 0.1960
0.4800, 1.0000, 0.2920, 0.1100, 0.2180, 0.1516, 0.3900, 0.6000, 0.4920, 0.0980, 0.2220
0.7900, 1.0000, 0.2700, 0.1030, 0.1690, 0.1108, 0.3700, 0.5000, 0.4663, 0.1100, 0.2770
0.4000, 0.0000, 0.3070, 0.0990, 0.1770, 0.0854, 0.5000, 0.4000, 0.5338, 0.0850, 0.0990
0.4900, 1.0000, 0.2880, 0.0920, 0.2070, 0.1400, 0.4400, 0.5000, 0.4745, 0.0920, 0.1960
0.5100, 0.0000, 0.3060, 0.1030, 0.1980, 0.1066, 0.5700, 0.3000, 0.5148, 0.1000, 0.2020
0.5700, 0.0000, 0.3010, 0.1170, 0.2020, 0.1396, 0.4200, 0.5000, 0.4625, 0.1200, 0.1550
0.5900, 1.0000, 0.2470, 0.1140, 0.1520, 0.1048, 0.2900, 0.5000, 0.4511, 0.0880, 0.0770
0.5100, 0.0000, 0.2770, 0.0990, 0.2290, 0.1456, 0.6900, 0.3000, 0.4277, 0.0770, 0.1910
0.7400, 0.0000, 0.2980, 0.1010, 0.1710, 0.1048, 0.5000, 0.3000, 0.4394, 0.0860, 0.0700
0.6700, 0.0000, 0.2670, 0.1050, 0.2250, 0.1354, 0.6900, 0.3000, 0.4635, 0.0960, 0.0730
0.4900, 0.0000, 0.1980, 0.0880, 0.1880, 0.1148, 0.5700, 0.3000, 0.4394, 0.0930, 0.0490
0.5700, 0.0000, 0.2330, 0.0880, 0.1550, 0.0636, 0.7800, 0.2000, 0.4205, 0.0780, 0.0650
0.5600, 1.0000, 0.3510, 0.1230, 0.1640, 0.0950, 0.3800, 0.4000, 0.5043, 0.1170, 0.2630
0.5200, 1.0000, 0.2970, 0.1090, 0.2280, 0.1628, 0.3100, 0.8000, 0.5142, 0.1030, 0.2480
0.6900, 0.0000, 0.2930, 0.1240, 0.2230, 0.1390, 0.5400, 0.4000, 0.5011, 0.1020, 0.2960
0.3700, 0.0000, 0.2030, 0.0830, 0.1850, 0.1246, 0.3800, 0.5000, 0.4719, 0.0880, 0.2140
0.2400, 0.0000, 0.2250, 0.0890, 0.1410, 0.0680, 0.5200, 0.3000, 0.4654, 0.0840, 0.1850
0.5500, 1.0000, 0.2270, 0.0930, 0.1540, 0.0942, 0.5300, 0.3000, 0.3526, 0.0750, 0.0780
0.3600, 0.0000, 0.2280, 0.0870, 0.1780, 0.1160, 0.4100, 0.4000, 0.4654, 0.0820, 0.0930
0.4200, 1.0000, 0.2400, 0.1070, 0.1500, 0.0850, 0.4400, 0.3000, 0.4654, 0.0960, 0.2520
0.2100, 0.0000, 0.2420, 0.0760, 0.1470, 0.0770, 0.5300, 0.3000, 0.4443, 0.0790, 0.1500
0.4100, 0.0000, 0.2020, 0.0620, 0.1530, 0.0890, 0.5000, 0.3000, 0.4249, 0.0890, 0.0770
0.5700, 1.0000, 0.2940, 0.1090, 0.1600, 0.0876, 0.3100, 0.5000, 0.5333, 0.0920, 0.2080
0.2000, 1.0000, 0.2210, 0.0870, 0.1710, 0.0996, 0.5800, 0.3000, 0.4205, 0.0780, 0.0770
0.6700, 1.0000, 0.2360, 0.1113, 0.1890, 0.1054, 0.7000, 0.2700, 0.4220, 0.0930, 0.1080
0.3400, 0.0000, 0.2520, 0.0770, 0.1890, 0.1206, 0.5300, 0.4000, 0.4344, 0.0790, 0.1600
0.4100, 1.0000, 0.2490, 0.0860, 0.1920, 0.1150, 0.6100, 0.3000, 0.4382, 0.0940, 0.0530
0.3800, 1.0000, 0.3300, 0.0780, 0.3010, 0.2150, 0.5000, 0.6020, 0.5193, 0.1080, 0.2200
0.5100, 0.0000, 0.2350, 0.1010, 0.1950, 0.1210, 0.5100, 0.4000, 0.4745, 0.0940, 0.1540
0.5200, 1.0000, 0.2640, 0.0913, 0.2180, 0.1520, 0.3900, 0.5590, 0.4905, 0.0990, 0.2590
0.6700, 0.0000, 0.2980, 0.0800, 0.1720, 0.0934, 0.6300, 0.3000, 0.4357, 0.0820, 0.0900
0.6100, 0.0000, 0.3000, 0.1080, 0.1940, 0.1000, 0.5200, 0.3730, 0.5347, 0.1050, 0.2460
0.6700, 1.0000, 0.2500, 0.1117, 0.1460, 0.0934, 0.3300, 0.4420, 0.4585, 0.1030, 0.1240
0.5600, 0.0000, 0.2700, 0.1050, 0.2470, 0.1606, 0.5400, 0.5000, 0.5088, 0.0940, 0.0670
0.6400, 0.0000, 0.2000, 0.0747, 0.1890, 0.1148, 0.6200, 0.3050, 0.4111, 0.0910, 0.0720
0.5800, 1.0000, 0.2550, 0.1120, 0.1630, 0.1106, 0.2900, 0.6000, 0.4762, 0.0860, 0.2570
0.5500, 0.0000, 0.2820, 0.0910, 0.2500, 0.1402, 0.6700, 0.4000, 0.5366, 0.1030, 0.2620
0.6200, 1.0000, 0.3330, 0.1140, 0.1820, 0.1140, 0.3800, 0.5000, 0.5011, 0.0960, 0.2750
0.5700, 1.0000, 0.2560, 0.0960, 0.2000, 0.1330, 0.5200, 0.3850, 0.4318, 0.1050, 0.1770
0.2000, 1.0000, 0.2420, 0.0880, 0.1260, 0.0722, 0.4500, 0.3000, 0.3784, 0.0740, 0.0710
0.5300, 1.0000, 0.2210, 0.0980, 0.1650, 0.1052, 0.4700, 0.4000, 0.4159, 0.0810, 0.0470
0.3200, 1.0000, 0.3140, 0.0890, 0.1530, 0.0842, 0.5600, 0.3000, 0.4159, 0.0900, 0.1870
0.4100, 0.0000, 0.2310, 0.0860, 0.1480, 0.0780, 0.5800, 0.3000, 0.4094, 0.0600, 0.1250
0.6000, 0.0000, 0.2340, 0.0767, 0.2470, 0.1480, 0.6500, 0.3800, 0.5136, 0.0770, 0.0780
0.2600, 0.0000, 0.1880, 0.0830, 0.1910, 0.1036, 0.6900, 0.3000, 0.4522, 0.0690, 0.0510
0.3700, 0.0000, 0.3080, 0.1120, 0.2820, 0.1972, 0.4300, 0.7000, 0.5342, 0.1010, 0.2580
0.4500, 0.0000, 0.3200, 0.1100, 0.2240, 0.1342, 0.4500, 0.5000, 0.5412, 0.0930, 0.2150
0.6700, 0.0000, 0.3160, 0.1160, 0.1790, 0.0904, 0.4100, 0.4000, 0.5472, 0.1000, 0.3030
0.3400, 1.0000, 0.3550, 0.1200, 0.2330, 0.1466, 0.3400, 0.7000, 0.5568, 0.1010, 0.2430
0.5000, 0.0000, 0.3190, 0.0783, 0.2070, 0.1492, 0.3800, 0.5450, 0.4595, 0.0840, 0.0910
0.7100, 0.0000, 0.2950, 0.0970, 0.2270, 0.1516, 0.4500, 0.5000, 0.5024, 0.1080, 0.1500
0.5700, 1.0000, 0.3160, 0.1170, 0.2250, 0.1076, 0.4000, 0.6000, 0.5958, 0.1130, 0.3100
0.4900, 0.0000, 0.2030, 0.0930, 0.1840, 0.1030, 0.6100, 0.3000, 0.4605, 0.0930, 0.1530
0.3500, 0.0000, 0.4130, 0.0810, 0.1680, 0.1028, 0.3700, 0.5000, 0.4949, 0.0940, 0.3460
0.4100, 1.0000, 0.2120, 0.1020, 0.1840, 0.1004, 0.6400, 0.3000, 0.4585, 0.0790, 0.0630
0.7000, 1.0000, 0.2410, 0.0823, 0.1940, 0.1492, 0.3100, 0.6260, 0.4234, 0.1050, 0.0890
0.5200, 0.0000, 0.2300, 0.1070, 0.1790, 0.1237, 0.4250, 0.4210, 0.4159, 0.0930, 0.0500
0.6000, 0.0000, 0.2560, 0.0780, 0.1950, 0.0954, 0.9100, 0.2000, 0.3761, 0.0870, 0.0390
0.6200, 0.0000, 0.2250, 0.1250, 0.2150, 0.0990, 0.9800, 0.2000, 0.4500, 0.0950, 0.1030
0.4400, 1.0000, 0.3820, 0.1230, 0.2010, 0.1266, 0.4400, 0.5000, 0.5024, 0.0920, 0.3080
0.2800, 1.0000, 0.1920, 0.0810, 0.1550, 0.0946, 0.5100, 0.3000, 0.3850, 0.0870, 0.1160
0.5800, 1.0000, 0.2900, 0.0850, 0.1560, 0.1092, 0.3600, 0.4000, 0.3989, 0.0860, 0.1450
0.3900, 1.0000, 0.2400, 0.0897, 0.1900, 0.1136, 0.5200, 0.3650, 0.4804, 0.1010, 0.0740
0.3400, 1.0000, 0.2060, 0.0980, 0.1830, 0.0920, 0.8300, 0.2000, 0.3689, 0.0920, 0.0450
0.6500, 0.0000, 0.2630, 0.0700, 0.2440, 0.1662, 0.5100, 0.5000, 0.4898, 0.0980, 0.1150
0.6600, 1.0000, 0.3460, 0.1150, 0.2040, 0.1394, 0.3600, 0.6000, 0.4963, 0.1090, 0.2640
0.5100, 0.0000, 0.2340, 0.0870, 0.2200, 0.1088, 0.9300, 0.2000, 0.4511, 0.0820, 0.0870
0.5000, 1.0000, 0.2920, 0.1190, 0.1620, 0.0852, 0.5400, 0.3000, 0.4736, 0.0950, 0.2020
0.5900, 1.0000, 0.2720, 0.1070, 0.1580, 0.1020, 0.3900, 0.4000, 0.4443, 0.0930, 0.1270
0.5200, 0.0000, 0.2700, 0.0783, 0.1340, 0.0730, 0.4400, 0.3050, 0.4443, 0.0690, 0.1820
0.6900, 1.0000, 0.2450, 0.1080, 0.2430, 0.1364, 0.4000, 0.6000, 0.5808, 0.1000, 0.2410
0.5300, 0.0000, 0.2410, 0.1050, 0.1840, 0.1134, 0.4600, 0.4000, 0.4812, 0.0950, 0.0660
0.4700, 1.0000, 0.2530, 0.0980, 0.1730, 0.1056, 0.4400, 0.4000, 0.4762, 0.1080, 0.0940
0.5200, 0.0000, 0.2880, 0.1130, 0.2800, 0.1740, 0.6700, 0.4000, 0.5273, 0.0860, 0.2830
0.3900, 0.0000, 0.2090, 0.0950, 0.1500, 0.0656, 0.6800, 0.2000, 0.4407, 0.0950, 0.0640
0.6700, 1.0000, 0.2300, 0.0700, 0.1840, 0.1280, 0.3500, 0.5000, 0.4654, 0.0990, 0.1020
0.5900, 1.0000, 0.2410, 0.0960, 0.1700, 0.0986, 0.5400, 0.3000, 0.4466, 0.0850, 0.2000
0.5100, 1.0000, 0.2810, 0.1060, 0.2020, 0.1222, 0.5500, 0.4000, 0.4820, 0.0870, 0.2650
0.2300, 1.0000, 0.1800, 0.0780, 0.1710, 0.0960, 0.4800, 0.4000, 0.4905, 0.0920, 0.0940
0.6800, 0.0000, 0.2590, 0.0930, 0.2530, 0.1812, 0.5300, 0.5000, 0.4543, 0.0980, 0.2300
0.4400, 0.0000, 0.2150, 0.0850, 0.1570, 0.0922, 0.5500, 0.3000, 0.3892, 0.0840, 0.1810
0.6000, 1.0000, 0.2430, 0.1030, 0.1410, 0.0866, 0.3300, 0.4000, 0.4673, 0.0780, 0.1560
0.5200, 0.0000, 0.2450, 0.0900, 0.1980, 0.1290, 0.2900, 0.7000, 0.5298, 0.0860, 0.2330
0.3800, 0.0000, 0.2130, 0.0720, 0.1650, 0.0602, 0.8800, 0.2000, 0.4431, 0.0900, 0.0600
0.6100, 0.0000, 0.2580, 0.0900, 0.2800, 0.1954, 0.5500, 0.5000, 0.4997, 0.0900, 0.2190
0.6800, 1.0000, 0.2480, 0.1010, 0.2210, 0.1514, 0.6000, 0.4000, 0.3871, 0.0870, 0.0800
0.2800, 1.0000, 0.3150, 0.0830, 0.2280, 0.1494, 0.3800, 0.6000, 0.5313, 0.0830, 0.0680
0.6500, 1.0000, 0.3350, 0.1020, 0.1900, 0.1262, 0.3500, 0.5000, 0.4970, 0.1020, 0.3320
0.6900, 0.0000, 0.2810, 0.1130, 0.2340, 0.1428, 0.5200, 0.4000, 0.5278, 0.0770, 0.2480
0.5100, 0.0000, 0.2430, 0.0853, 0.1530, 0.0716, 0.7100, 0.2150, 0.3951, 0.0820, 0.0840
0.2900, 0.0000, 0.3500, 0.0983, 0.2040, 0.1426, 0.5000, 0.4080, 0.4043, 0.0910, 0.2000
0.5500, 1.0000, 0.2350, 0.0930, 0.1770, 0.1268, 0.4100, 0.4000, 0.3829, 0.0830, 0.0550
0.3400, 1.0000, 0.3000, 0.0830, 0.1850, 0.1072, 0.5300, 0.3000, 0.4820, 0.0920, 0.0850
0.6700, 0.0000, 0.2070, 0.0830, 0.1700, 0.0998, 0.5900, 0.3000, 0.4025, 0.0770, 0.0890
0.4900, 0.0000, 0.2560, 0.0760, 0.1610, 0.0998, 0.5100, 0.3000, 0.3932, 0.0780, 0.0310
0.5500, 1.0000, 0.2290, 0.0810, 0.1230, 0.0672, 0.4100, 0.3000, 0.4304, 0.0880, 0.1290
0.5900, 1.0000, 0.2510, 0.0900, 0.1630, 0.1014, 0.4600, 0.4000, 0.4357, 0.0910, 0.0830
0.5300, 0.0000, 0.3320, 0.0827, 0.1860, 0.1068, 0.4600, 0.4040, 0.5112, 0.1020, 0.2750
0.4800, 1.0000, 0.2410, 0.1100, 0.2090, 0.1346, 0.5800, 0.4000, 0.4407, 0.1000, 0.0650
0.5200, 0.0000, 0.2950, 0.1043, 0.2110, 0.1328, 0.4900, 0.4310, 0.4984, 0.0980, 0.1980
0.6900, 0.0000, 0.2960, 0.1220, 0.2310, 0.1284, 0.5600, 0.4000, 0.5451, 0.0860, 0.2360
0.6000, 1.0000, 0.2280, 0.1100, 0.2450, 0.1898, 0.3900, 0.6000, 0.4394, 0.0880, 0.2530
0.4600, 1.0000, 0.2270, 0.0830, 0.1830, 0.1258, 0.3200, 0.6000, 0.4836, 0.0750, 0.1240
0.5100, 1.0000, 0.2620, 0.1010, 0.1610, 0.0996, 0.4800, 0.3000, 0.4205, 0.0880, 0.0440
0.6700, 1.0000, 0.2350, 0.0960, 0.2070, 0.1382, 0.4200, 0.5000, 0.4898, 0.1110, 0.1720
0.4900, 0.0000, 0.2210, 0.0850, 0.1360, 0.0634, 0.6200, 0.2190, 0.3970, 0.0720, 0.1140
0.4600, 1.0000, 0.2650, 0.0940, 0.2470, 0.1602, 0.5900, 0.4000, 0.4935, 0.1110, 0.1420
0.4700, 0.0000, 0.3240, 0.1050, 0.1880, 0.1250, 0.4600, 0.4090, 0.4443, 0.0990, 0.1090
0.7500, 0.0000, 0.3010, 0.0780, 0.2220, 0.1542, 0.4400, 0.5050, 0.4779, 0.0970, 0.1800
0.2800, 0.0000, 0.2420, 0.0930, 0.1740, 0.1064, 0.5400, 0.3000, 0.4220, 0.0840, 0.1440
0.6500, 1.0000, 0.3130, 0.1100, 0.2130, 0.1280, 0.4700, 0.5000, 0.5247, 0.0910, 0.1630
0.4200, 0.0000, 0.3010, 0.0910, 0.1820, 0.1148, 0.4900, 0.4000, 0.4511, 0.0820, 0.1470
0.5100, 0.0000, 0.2450, 0.0790, 0.2120, 0.1286, 0.6500, 0.3000, 0.4522, 0.0910, 0.0970
0.5300, 1.0000, 0.2770, 0.0950, 0.1900, 0.1018, 0.4100, 0.5000, 0.5464, 0.1010, 0.2200
0.5400, 0.0000, 0.2320, 0.1107, 0.2380, 0.1628, 0.4800, 0.4960, 0.4913, 0.1080, 0.1900
0.7300, 0.0000, 0.2700, 0.1020, 0.2110, 0.1210, 0.6700, 0.3000, 0.4745, 0.0990, 0.1090
0.5400, 0.0000, 0.2680, 0.1080, 0.1760, 0.0806, 0.6700, 0.3000, 0.4956, 0.1060, 0.1910
0.4200, 0.0000, 0.2920, 0.0930, 0.2490, 0.1742, 0.4500, 0.6000, 0.5004, 0.0920, 0.1220
0.7500, 0.0000, 0.3120, 0.1177, 0.2290, 0.1388, 0.2900, 0.7900, 0.5724, 0.1060, 0.2300
0.5500, 1.0000, 0.3210, 0.1127, 0.2070, 0.0924, 0.2500, 0.8280, 0.6105, 0.1110, 0.2420
0.6800, 1.0000, 0.2570, 0.1090, 0.2330, 0.1126, 0.3500, 0.7000, 0.6057, 0.1050, 0.2480
0.5700, 0.0000, 0.2690, 0.0980, 0.2460, 0.1652, 0.3800, 0.7000, 0.5366, 0.0960, 0.2490
0.4800, 0.0000, 0.3140, 0.0753, 0.2420, 0.1516, 0.3800, 0.6370, 0.5568, 0.1030, 0.1920
0.6100, 1.0000, 0.2560, 0.0850, 0.1840, 0.1162, 0.3900, 0.5000, 0.4970, 0.0980, 0.1310
0.6900, 0.0000, 0.3700, 0.1030, 0.2070, 0.1314, 0.5500, 0.4000, 0.4635, 0.0900, 0.2370
0.3800, 0.0000, 0.3260, 0.0770, 0.1680, 0.1006, 0.4700, 0.4000, 0.4625, 0.0960, 0.0780
0.4500, 1.0000, 0.2120, 0.0940, 0.1690, 0.0968, 0.5500, 0.3000, 0.4454, 0.1020, 0.1350
0.5100, 1.0000, 0.2920, 0.1070, 0.1870, 0.1390, 0.3200, 0.6000, 0.4382, 0.0950, 0.2440
0.7100, 1.0000, 0.2400, 0.0840, 0.1380, 0.0858, 0.3900, 0.4000, 0.4190, 0.0900, 0.1990
0.5700, 0.0000, 0.3610, 0.1170, 0.1810, 0.1082, 0.3400, 0.5000, 0.5268, 0.1000, 0.2700
0.5600, 1.0000, 0.2580, 0.1030, 0.1770, 0.1144, 0.3400, 0.5000, 0.4963, 0.0990, 0.1640
0.3200, 1.0000, 0.2200, 0.0880, 0.1370, 0.0786, 0.4800, 0.3000, 0.3951, 0.0780, 0.0720
0.5000, 0.0000, 0.2190, 0.0910, 0.1900, 0.1112, 0.6700, 0.3000, 0.4078, 0.0770, 0.0960
0.4300, 0.0000, 0.3430, 0.0840, 0.2560, 0.1726, 0.3300, 0.8000, 0.5529, 0.1040, 0.3060
0.5400, 1.0000, 0.2520, 0.1150, 0.1810, 0.1200, 0.3900, 0.5000, 0.4701, 0.0920, 0.0910
0.3100, 0.0000, 0.2330, 0.0850, 0.1900, 0.1308, 0.4300, 0.4000, 0.4394, 0.0770, 0.2140
0.5600, 0.0000, 0.2570, 0.0800, 0.2440, 0.1516, 0.5900, 0.4000, 0.5118, 0.0950, 0.0950
0.4400, 0.0000, 0.2510, 0.1330, 0.1820, 0.1130, 0.5500, 0.3000, 0.4249, 0.0840, 0.2160
0.5700, 1.0000, 0.3190, 0.1110, 0.1730, 0.1162, 0.4100, 0.4000, 0.4369, 0.0870, 0.2630

Test data:

# diabetes_norm_test_100.txt
#
0.6400, 1.0000, 0.2840, 0.1110, 0.1840, 0.1270, 0.4100, 0.4000, 0.4382, 0.0970, 0.1780
0.4300, 0.0000, 0.2810, 0.1210, 0.1920, 0.1210, 0.6000, 0.3000, 0.4007, 0.0930, 0.1130
0.1900, 0.0000, 0.2530, 0.0830, 0.2250, 0.1566, 0.4600, 0.5000, 0.4719, 0.0840, 0.2000
0.7100, 1.0000, 0.2610, 0.0850, 0.2200, 0.1524, 0.4700, 0.5000, 0.4635, 0.0910, 0.1390
0.5000, 1.0000, 0.2800, 0.1040, 0.2820, 0.1968, 0.4400, 0.6000, 0.5328, 0.0950, 0.1390
0.5900, 1.0000, 0.2360, 0.0730, 0.1800, 0.1074, 0.5100, 0.4000, 0.4682, 0.0840, 0.0880
0.5700, 0.0000, 0.2450, 0.0930, 0.1860, 0.0966, 0.7100, 0.3000, 0.4522, 0.0910, 0.1480
0.4900, 1.0000, 0.2100, 0.0820, 0.1190, 0.0854, 0.2300, 0.5000, 0.3970, 0.0740, 0.0880
0.4100, 1.0000, 0.3200, 0.1260, 0.1980, 0.1042, 0.4900, 0.4000, 0.5412, 0.1240, 0.2430
0.2500, 1.0000, 0.2260, 0.0850, 0.1300, 0.0710, 0.4800, 0.3000, 0.4007, 0.0810, 0.0710
0.5200, 1.0000, 0.1970, 0.0810, 0.1520, 0.0534, 0.8200, 0.2000, 0.4419, 0.0820, 0.0770
0.3400, 0.0000, 0.2120, 0.0840, 0.2540, 0.1134, 0.5200, 0.5000, 0.6094, 0.0920, 0.1090
0.4200, 1.0000, 0.3060, 0.1010, 0.2690, 0.1722, 0.5000, 0.5000, 0.5455, 0.1060, 0.2720
0.2800, 1.0000, 0.2550, 0.0990, 0.1620, 0.1016, 0.4600, 0.4000, 0.4277, 0.0940, 0.0600
0.4700, 1.0000, 0.2330, 0.0900, 0.1950, 0.1258, 0.5400, 0.4000, 0.4331, 0.0730, 0.0540
0.3200, 1.0000, 0.3100, 0.1000, 0.1770, 0.0962, 0.4500, 0.4000, 0.5187, 0.0770, 0.2210
0.4300, 0.0000, 0.1850, 0.0870, 0.1630, 0.0936, 0.6100, 0.2670, 0.3738, 0.0800, 0.0900
0.5900, 1.0000, 0.2690, 0.1040, 0.1940, 0.1266, 0.4300, 0.5000, 0.4804, 0.1060, 0.3110
0.5300, 0.0000, 0.2830, 0.1010, 0.1790, 0.1070, 0.4800, 0.4000, 0.4788, 0.1010, 0.2810
0.6000, 0.0000, 0.2570, 0.1030, 0.1580, 0.0846, 0.6400, 0.2000, 0.3850, 0.0970, 0.1820
0.5400, 1.0000, 0.3610, 0.1150, 0.1630, 0.0984, 0.4300, 0.4000, 0.4682, 0.1010, 0.3210
0.3500, 1.0000, 0.2410, 0.0947, 0.1550, 0.0974, 0.3200, 0.4840, 0.4852, 0.0940, 0.0580
0.4900, 1.0000, 0.2580, 0.0890, 0.1820, 0.1186, 0.3900, 0.5000, 0.4804, 0.1150, 0.2620
0.5800, 0.0000, 0.2280, 0.0910, 0.1960, 0.1188, 0.4800, 0.4000, 0.4984, 0.1150, 0.2060
0.3600, 1.0000, 0.3910, 0.0900, 0.2190, 0.1358, 0.3800, 0.6000, 0.5421, 0.1030, 0.2330
0.4600, 1.0000, 0.4220, 0.0990, 0.2110, 0.1370, 0.4400, 0.5000, 0.5011, 0.0990, 0.2420
0.4400, 1.0000, 0.2660, 0.0990, 0.2050, 0.1090, 0.4300, 0.5000, 0.5580, 0.1110, 0.1230
0.4600, 0.0000, 0.2990, 0.0830, 0.1710, 0.1130, 0.3800, 0.4500, 0.4585, 0.0980, 0.1670
0.5400, 0.0000, 0.2100, 0.0780, 0.1880, 0.1074, 0.7000, 0.3000, 0.3970, 0.0730, 0.0630
0.6300, 1.0000, 0.2550, 0.1090, 0.2260, 0.1032, 0.4600, 0.5000, 0.5951, 0.0870, 0.1970
0.4100, 1.0000, 0.2420, 0.0900, 0.1990, 0.1236, 0.5700, 0.4000, 0.4522, 0.0860, 0.0710
0.2800, 0.0000, 0.2540, 0.0930, 0.1410, 0.0790, 0.4900, 0.3000, 0.4174, 0.0910, 0.1680
0.1900, 0.0000, 0.2320, 0.0750, 0.1430, 0.0704, 0.5200, 0.3000, 0.4635, 0.0720, 0.1400
0.6100, 1.0000, 0.2610, 0.1260, 0.2150, 0.1298, 0.5700, 0.4000, 0.4949, 0.0960, 0.2170
0.4800, 0.0000, 0.3270, 0.0930, 0.2760, 0.1986, 0.4300, 0.6420, 0.5148, 0.0910, 0.1210
0.5400, 1.0000, 0.2730, 0.1000, 0.2000, 0.1440, 0.3300, 0.6000, 0.4745, 0.0760, 0.2350
0.5300, 1.0000, 0.2660, 0.0930, 0.1850, 0.1224, 0.3600, 0.5000, 0.4890, 0.0820, 0.2450
0.4800, 0.0000, 0.2280, 0.1010, 0.1100, 0.0416, 0.5600, 0.2000, 0.4127, 0.0970, 0.0400
0.5300, 0.0000, 0.2880, 0.1117, 0.1450, 0.0872, 0.4600, 0.3150, 0.4078, 0.0850, 0.0520
0.2900, 1.0000, 0.1810, 0.0730, 0.1580, 0.0990, 0.4100, 0.4000, 0.4500, 0.0780, 0.1040
0.6200, 0.0000, 0.3200, 0.0880, 0.1720, 0.0690, 0.3800, 0.4000, 0.5784, 0.1000, 0.1320
0.5000, 1.0000, 0.2370, 0.0920, 0.1660, 0.0970, 0.5200, 0.3000, 0.4443, 0.0930, 0.0880
0.5800, 1.0000, 0.2360, 0.0960, 0.2570, 0.1710, 0.5900, 0.4000, 0.4905, 0.0820, 0.0690
0.5500, 1.0000, 0.2460, 0.1090, 0.1430, 0.0764, 0.5100, 0.3000, 0.4357, 0.0880, 0.2190
0.5400, 0.0000, 0.2260, 0.0900, 0.1830, 0.1042, 0.6400, 0.3000, 0.4304, 0.0920, 0.0720
0.3600, 0.0000, 0.2780, 0.0730, 0.1530, 0.1044, 0.4200, 0.4000, 0.3497, 0.0730, 0.2010
0.6300, 1.0000, 0.2410, 0.1110, 0.1840, 0.1122, 0.4400, 0.4000, 0.4935, 0.0820, 0.1100
0.4700, 1.0000, 0.2650, 0.0700, 0.1810, 0.1048, 0.6300, 0.3000, 0.4190, 0.0700, 0.0510
0.5100, 1.0000, 0.3280, 0.1120, 0.2020, 0.1006, 0.3700, 0.5000, 0.5775, 0.1090, 0.2770
0.4200, 0.0000, 0.1990, 0.0760, 0.1460, 0.0832, 0.5500, 0.3000, 0.3664, 0.0790, 0.0630
0.3700, 1.0000, 0.2360, 0.0940, 0.2050, 0.1388, 0.5300, 0.4000, 0.4190, 0.1070, 0.1180
0.2800, 0.0000, 0.2210, 0.0820, 0.1680, 0.1006, 0.5400, 0.3000, 0.4205, 0.0860, 0.0690
0.5800, 0.0000, 0.2810, 0.1110, 0.1980, 0.0806, 0.3100, 0.6000, 0.6068, 0.0930, 0.2730
0.3200, 0.0000, 0.2650, 0.0860, 0.1840, 0.1016, 0.5300, 0.4000, 0.4990, 0.0780, 0.2580
0.2500, 1.0000, 0.2350, 0.0880, 0.1430, 0.0808, 0.5500, 0.3000, 0.3584, 0.0830, 0.0430
0.6300, 0.0000, 0.2600, 0.0857, 0.1550, 0.0782, 0.4600, 0.3370, 0.5037, 0.0970, 0.1980
0.5200, 0.0000, 0.2780, 0.0850, 0.2190, 0.1360, 0.4900, 0.4000, 0.5136, 0.0750, 0.2420
0.6500, 1.0000, 0.2850, 0.1090, 0.2010, 0.1230, 0.4600, 0.4000, 0.5075, 0.0960, 0.2320
0.4200, 0.0000, 0.3060, 0.1210, 0.1760, 0.0928, 0.6900, 0.3000, 0.4263, 0.0890, 0.1750
0.5300, 0.0000, 0.2220, 0.0780, 0.1640, 0.0810, 0.7000, 0.2000, 0.4174, 0.1010, 0.0930
0.7900, 1.0000, 0.2330, 0.0880, 0.1860, 0.1284, 0.3300, 0.6000, 0.4812, 0.1020, 0.1680
0.4300, 0.0000, 0.3540, 0.0930, 0.1850, 0.1002, 0.4400, 0.4000, 0.5318, 0.1010, 0.2750
0.4400, 0.0000, 0.3140, 0.1150, 0.1650, 0.0976, 0.5200, 0.3000, 0.4344, 0.0890, 0.2930
0.6200, 1.0000, 0.3780, 0.1190, 0.1130, 0.0510, 0.3100, 0.4000, 0.5043, 0.0840, 0.2810
0.3300, 0.0000, 0.1890, 0.0700, 0.1620, 0.0918, 0.5900, 0.3000, 0.4025, 0.0580, 0.0720
0.5600, 0.0000, 0.3500, 0.0793, 0.1950, 0.1408, 0.4200, 0.4640, 0.4111, 0.0960, 0.1400
0.6600, 0.0000, 0.2170, 0.1260, 0.2120, 0.1278, 0.4500, 0.4710, 0.5278, 0.1010, 0.1890
0.3400, 1.0000, 0.2530, 0.1110, 0.2300, 0.1620, 0.3900, 0.6000, 0.4977, 0.0900, 0.1810
0.4600, 1.0000, 0.2380, 0.0970, 0.2240, 0.1392, 0.4200, 0.5000, 0.5366, 0.0810, 0.2090
0.5000, 0.0000, 0.3180, 0.0820, 0.1360, 0.0692, 0.5500, 0.2000, 0.4078, 0.0850, 0.1360
0.6900, 0.0000, 0.3430, 0.1130, 0.2000, 0.1238, 0.5400, 0.4000, 0.4710, 0.1120, 0.2610
0.3400, 0.0000, 0.2630, 0.0870, 0.1970, 0.1200, 0.6300, 0.3000, 0.4249, 0.0960, 0.1130
0.7100, 1.0000, 0.2700, 0.0933, 0.2690, 0.1902, 0.4100, 0.6560, 0.5242, 0.0930, 0.1310
0.4700, 0.0000, 0.2720, 0.0800, 0.2080, 0.1456, 0.3800, 0.6000, 0.4804, 0.0920, 0.1740
0.4100, 0.0000, 0.3380, 0.1233, 0.1870, 0.1270, 0.4500, 0.4160, 0.4318, 0.1000, 0.2570
0.3400, 0.0000, 0.3300, 0.0730, 0.1780, 0.1146, 0.5100, 0.3490, 0.4127, 0.0920, 0.0550
0.5100, 0.0000, 0.2410, 0.0870, 0.2610, 0.1756, 0.6900, 0.4000, 0.4407, 0.0930, 0.0840
0.4300, 0.0000, 0.2130, 0.0790, 0.1410, 0.0788, 0.5300, 0.3000, 0.3829, 0.0900, 0.0420
0.5500, 0.0000, 0.2300, 0.0947, 0.1900, 0.1376, 0.3800, 0.5000, 0.4277, 0.1060, 0.1460
0.5900, 1.0000, 0.2790, 0.1010, 0.2180, 0.1442, 0.3800, 0.6000, 0.5187, 0.0950, 0.2120
0.2700, 1.0000, 0.3360, 0.1100, 0.2460, 0.1566, 0.5700, 0.4000, 0.5088, 0.0890, 0.2330
0.5100, 1.0000, 0.2270, 0.1030, 0.2170, 0.1624, 0.3000, 0.7000, 0.4812, 0.0800, 0.0910
0.4900, 1.0000, 0.2740, 0.0890, 0.1770, 0.1130, 0.3700, 0.5000, 0.4905, 0.0970, 0.1110
0.2700, 0.0000, 0.2260, 0.0710, 0.1160, 0.0434, 0.5600, 0.2000, 0.4419, 0.0790, 0.1520
0.5700, 1.0000, 0.2320, 0.1073, 0.2310, 0.1594, 0.4100, 0.5630, 0.5030, 0.1120, 0.1200
0.3900, 1.0000, 0.2690, 0.0930, 0.1360, 0.0754, 0.4800, 0.3000, 0.4143, 0.0990, 0.0670
0.6200, 1.0000, 0.3460, 0.1200, 0.2150, 0.1292, 0.4300, 0.5000, 0.5366, 0.1230, 0.3100
0.3700, 0.0000, 0.2330, 0.0880, 0.2230, 0.1420, 0.6500, 0.3400, 0.4357, 0.0820, 0.0940
0.4600, 0.0000, 0.2110, 0.0800, 0.2050, 0.1444, 0.4200, 0.5000, 0.4533, 0.0870, 0.1830
0.6800, 1.0000, 0.2350, 0.1010, 0.1620, 0.0854, 0.5900, 0.3000, 0.4477, 0.0910, 0.0660
0.5100, 0.0000, 0.3150, 0.0930, 0.2310, 0.1440, 0.4900, 0.4700, 0.5252, 0.1170, 0.1730
0.4100, 0.0000, 0.2080, 0.0860, 0.2230, 0.1282, 0.8300, 0.3000, 0.4078, 0.0890, 0.0720
0.5300, 0.0000, 0.2650, 0.0970, 0.1930, 0.1224, 0.5800, 0.3000, 0.4143, 0.0990, 0.0490
0.4500, 0.0000, 0.2420, 0.0830, 0.1770, 0.1184, 0.4500, 0.4000, 0.4220, 0.0820, 0.0640
0.3300, 0.0000, 0.1950, 0.0800, 0.1710, 0.0854, 0.7500, 0.2000, 0.3970, 0.0800, 0.0480
0.6000, 1.0000, 0.2820, 0.1120, 0.1850, 0.1138, 0.4200, 0.4000, 0.4984, 0.0930, 0.1780
0.4700, 1.0000, 0.2490, 0.0750, 0.2250, 0.1660, 0.4200, 0.5000, 0.4443, 0.1020, 0.1040
0.6000, 1.0000, 0.2490, 0.0997, 0.1620, 0.1066, 0.4300, 0.3770, 0.4127, 0.0950, 0.1320
0.3600, 0.0000, 0.3000, 0.0950, 0.2010, 0.1252, 0.4200, 0.4790, 0.5130, 0.0850, 0.2200
0.3600, 0.0000, 0.1960, 0.0710, 0.2500, 0.1332, 0.9700, 0.3000, 0.4595, 0.0920, 0.0570

Bottom line: I did a short experiment to compare support vector regression (SVR) with post-training-trimmed kernel ridge regression (KRR). I used the scikit library SVR and KernelRidge modules. Because of the nearly infinite number of hyperparameter values involved, it wasn’t possible to draw a strong conclusion, but my results strongly suggest the two techniques are essentially the same, or at least very similar, from a practical point of view.

Bear with me. The goal of a machine learning regression problem is to predict a single numeric value. For example, a bank might want to predict a maximum loan amount based on applicant age, sex, annual income, debt, and so on.

Common regression techniques include linear regression, quadratic regression, nearest neighbors regression, kernel ridge regression, Gaussian process regression, kernel support vector regression, neural network regression, random forest regression, and gradient boost regression. Each technique has dozens of variations, and each technique has pros and cons.

Two closely related machine learning regression techniques are kernel ridge regression (KRR) and support vector regression (SVR). Both techniques use a kernel function (usually the radial basis function, RBF) to compare two data items for similarity. Both techniques must store training data in order to make predictions. KRR must store all training items, while SVR eliminates some of the items during training, leaving just the “support vectors” that need to be stored. So, SVR uses less memory than KRR.

On the other hand, the loss function used by SVR is not differentiable, so SVR cannot be trained using stochastic gradient descent, and therefore, SVR does not scale well to very large datasets. So, KRR is easier to train than SVR.

Note: In addition to the kernel support vector regression technique discussed in this blog post, there is a linear support vector regression technique which is essentially useless in practice.

The idea of combining KRR and SVR goes like this: Briefly, I train a KRR model as normal using all data. Then I identify training data items that are predicted “too well” and remove them, leaving just pseudo support vectors. The somewhat unobvious SVR idea is that items that are predicted too well don’t help model accuracy very much, and can lead to an overfitted model. After removing some training items, I retrain a new KRR model using only the reduced training data. This gives a trimmed/sparse KRR model that approximates an SVR model.

In my mind, this technique gives the advantages of KRR (ability to handle very large datasets via SGD training) and the advantages of SVR (fewer stored model items and weights than KRR).

I first implemented the idea using the scikit KernelRidge module and the idea seemed to work well. But I wanted to take a second look, using a very small dataset, as a sanity check to make sure there weren’t any unexpected, bad, surprises. The output of one of the experiments is:

Begin SVR vs. trimmed KRR demo

Creating 20-item, 5-feature train data

X:
[[ 0.0458 -0.1872  1.4694 -1.4544  1.5328]
 [ 0.9008  0.4657  1.4883 -1.1651 -1.5362]
 [ 0.6536  0.8644  2.2698 -2.5530 -0.7422]
 [ 0.4002  0.9787  1.8676  1.7641  2.2409]
 [ 0.3869 -0.5108 -0.0282 -0.8955 -1.1806]
 [ 1.2303  1.2024 -0.3023  0.1563 -0.3873]
 [ 1.4543  0.7610  0.4439  0.1440  0.1217]
 [ 1.4941 -0.2052 -0.8541  0.3337  0.3131]
 [-0.3596 -0.8131  0.1774 -0.6725 -1.7263]
 [ 1.1788 -0.1799  1.0545  1.8959 -1.0708]
 [ 0.1290  1.1394  0.4023  0.7291 -1.2348]
 [ 0.9501 -0.1514  0.4106 -0.9773 -0.1032]
 [ 1.2224  0.2083  0.3564 -0.4032  0.9766]
 [-1.6302  0.4628  0.0519 -0.4018 -0.9073]
 [ 0.3782 -0.8878 -0.3479  0.1549 -1.9808]
 [ 0.0665  0.3025 -0.3627  0.4283 -0.6343]
 [ 0.0105  1.7859  0.4020  0.7066  0.1269]
 [-1.4200 -1.7063 -0.5097 -1.0486  1.9508]
 [-1.2528  0.7775 -0.2127 -0.4381 -1.6139]
 [-0.8708 -0.5788  0.0562 -0.6848 -0.3116]]

Creating and training SVR model
gamma = 0.1000
C = 1000.0000
epsilon = 8.0000
Done

Number support vectors: 10

Support vector indices:
[ 0  1  3  9 10 14 16 17 18 19]

Accuracy (within 0.10) train = 0.6000
MSE train = 64.0016
R2 train = 0.996314

===============================

Creating and training preliminary KRR RBF model
Setting gamma = 0.1000
Setting alpha = 0.0010
Done

Removing non-pseudo-support vectors
Using KRR trim epsilon = 0.1000

Number of pseudo support vectors = 10

Support vector indices:
[ 1  3  9 10 11 15 16 17 18 19]

Re-training trimmed KRR model
Done

Accuracy (within 0.10) train = 1.0000
MSE train = 0.0225
R2 train = 0.999999

End demo

The demo program begins by using the scikit make_regression() function to create a tiny synthetic dataset with just 20 rows/items, each with 5 predictor values. An SVR model ended up with 10 support vectors and an R2 score (essentially a scaled accuracy metric) of 0.9963 on the training data.

I tuned a trimmed KRR model to one with 10 pseudo-support vectors. The two techniques had 8 out of 10 support vectors in common — that’s good.

The trimmed KRR model had an R2 score of 0.9999 on the training data. The trimmed KRR model had better MSE than the SVR model, but that was expected because KRR minimizes MSE and SVR does not. The much better accuracy of the trimmed KRR model (100% for KRR vs. 60% for SVR) isn’t significant because the dataset is so small, and I didn’t use a test dataset to measure possible overfitting.

I noticed that both models were ultra-sensitive to hyperparameter values — gamma, C, and epsilon for SVR, and gamma, alpha, and trim-epsilon for trimmed KRR. This is a major weakness of both techniques.

Anyway, the sanity check was successful. It is possible to approximate a SVR regression model using a trimmed KRR model.

It’s common for me to refactor the software systems I create many times. It’s rarely possible to a get a non-trivial system completely correct on the first effort, and so a system is usually a collection of software sequels, so to speak, where each sequel is a bit better than its predecessor.

Right: In “Quatermass 2” aka “Enemy From Space” (1957), Quatermass discovers an alien invasion. The aliens use parasites to control the people in a small village and use the villagers to construct a plant to create alien food to support the invasion. Quatermass and the UK military blow up the plant and defeat the alien’s plans. My personal grade = A-.

Demo program. Replace the “lt” (less than) and “gt” with the Boolean operator symbols. (My blog editor chokes on symbols).

# svr_vs_krr_trimmed_scikit.py
# train using KRR, remove some, retrain using KRR

import numpy as np
from sklearn.kernel_ridge import KernelRidge
from sklearn.svm import SVR
from sklearn.datasets import make_regression

# KernelRidge(alpha=1, *, kernel='linear', gamma=None,
# degree=3, coef0=1, kernel_params=None)

# SVR(*, kernel='rbf', degree=3, gamma='scale',
# coef0=0.0, tol=0.001, C=1.0, epsilon=0.1,
# shrinking=True, cache_size=200, verbose=False,
# max_iter=-1)

# make_regression(n_samples=100, n_features=100,
# *, n_informative=10, n_targets=1, bias=0.0,
# effective_rank=None, tail_strength=0.5, noise=0.0,
# shuffle=True, coef=False, random_state=None)

# -----------------------------------------------------------

np.set_printoptions(precision=4, suppress=True,
  floatmode='fixed', linewidth=60)

# -----------------------------------------------------------

def accuracy(model, data_X, data_y, pct_close):
  n = len(data_X)
  n_correct = 0; n_wrong = 0
  for i in range(n):
    x = data_X[i].reshape(1,-1)
    y = data_y[i]
    y_pred = model.predict(x)[0]

    if np.abs(y - y_pred) "lt" np.abs(y * pct_close):
      n_correct += 1
    else: 
      n_wrong += 1
  return n_correct / (n_correct + n_wrong)

def mse(model, data_X, data_y):
  n = len(data_X)
  sum = 0.0
  for i in range(n):
    actual_y = data_y[i]
    pred_y = model.predict(data_X[i].reshape(1, -1))[0]
    diff = actual_y - pred_y
    sum += diff * diff
  return sum /n

# -----------------------------------------------------------
# -----------------------------------------------------------

print("\nBegin SVR vs. trimmmed KRR demo ")

np.set_printoptions(precision=4, suppress=True,
    floatmode='fixed')

print("\nCreating 20-item, 5-feature train data ")
X, y = make_regression(n_samples=20, n_features=5,
  n_informative=5, noise=0, random_state=0)

print("\nX: ")
print(X)

print("\nCreating and training SVR model ")
svr_gamma = 0.10
svr_C = 1000.0
svr_epsilon = 8.0
print("gamma = %0.4f " % svr_gamma)
print("C = %0.4f " % svr_C)
print("epsilon = %0.4f " % svr_epsilon)
svr_model = SVR(kernel='rbf', gamma=svr_gamma, C=svr_C,
  epsilon = svr_epsilon)
svr_model.fit(X, y)
print("Done ")

print("\nNumber support vectors: ", end="")
print(len(svr_model.support_))
print("\nSupport vector indices: ")
print(svr_model.support_)

X_sv = X[svr_model.support_,:]
y_sv = y[svr_model.support_]

acc_train = accuracy(svr_model, X_sv, y_sv, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
mse_train = mse(svr_model, X_sv, y_sv)
print("MSE train = %0.4f " % mse_train)
svr_r2 = svr_model.score(X_sv, y_sv)
print("R2 train = %0.6f " % svr_r2)

print("\n=============================== ")

print("\nCreating and training preliminary KRR model ")
krr_gamma = 0.1000
krr_alpha = 0.0010
print("Setting gamma = %0.4f " % krr_gamma)
print("Setting alpha = %0.4f " % krr_alpha)
model = KernelRidge(kernel='rbf', gamma=krr_gamma,
  alpha=krr_alpha)
model.fit(X, y)
print("Done ")

print("\nRemoving non-pseudo-support vectors ")
krr_trim_epsilon = 0.10
print("Using KRR trim epsilon = %0.4f " % krr_trim_epsilon)
# smaller epsilon = more support vectors
# larger epsilon = fewer support vectors

predictions = model.predict(X)
residuals = np.abs(y - predictions)
# keep only pts outside epsilon-tube (pseudo support vecs)
sv_indices = np.where(residuals "gt" krr_trim_epsilon)[0]
X_sv = X[sv_indices]
y_sv = y[sv_indices]
print("\nNumber of pseudo support vectors = " + \
  str(len(X_sv)))
print("\nSupport vector indices: ")
print(sv_indices)

# retrain
print("\nRe-training trimmed KRR model ")
krr_model = KernelRidge(kernel='rbf', 
  gamma=krr_gamma, alpha=krr_alpha)
krr_model.fit(X_sv, y_sv)
print("Done ")

acc_train = accuracy(krr_model, X_sv, y_sv, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
mse_train = mse(krr_model, X_sv, y_sv)
print("MSE train = %0.4f " % mse_train)
krr_r2 = krr_model.score(X_sv, y_sv)
print("R2 train = %0.6f " % krr_r2)

print("\nEnd demo ")

I’ve worked with machine learning for decades. In my opinion, one of the least understood topics is cross-validation. I’ll cut to the chase and say that using cross-validation is never a good idea. Frankly, I am astonished that cross-validation techniques exists at all.

Well, let me temper all that by saying for the scenarios I work in, cross-validation is never useful. Some of my colleagues tell me they use cross-validation.

There are so many significant reasons not to use cross-validation, that listing them all would take several blog posts. But I’ll list just a few, any one of which is good reason to never use cross-validation.

To begin with, and set context, there are two categories of cross-validation: k-fold cross validation, and leave-one-out cross validation. Technically, leave-one-out is a specific type of k-fold, but in practice they are used differently. And then there are two possible reasons to use cross-validation: for evaluation of model generalizability, and for model hyperparameter tuning.

Let me dispense with leave-one-out cross validation. Suppose you have n training items, let’s say 200. For leave-one-out cross validation, you create and train 200 models using 199 training items and 1 test item.

Note: One exception to having to train n models is leave-one-out cross-validation for ridge regression. It’s possible to use a math trick to just train the model once instead of n times. But this trick only works for ridge regression, a relatively weak regression technique.

If you are trying to use the leave-one-out cross-validation for hyperparameter tuning, this makes no sense whatsoever, because all the models are being trained on almost exactly the same data (except for one item) and your evaluation metrics are all based on the MSE or R2 or whatever of a single data item.

If you are trying to use the leave-one-out cross-validation to measure model generalizability, you must average the MSE or R2 of 200 values, each of which was computed on a single data item, which makes no sense. And even if you did do this, you still need to measure generalizability using a hold-out test set that wasn’t part of the cross-validation process. I am stunned that leave-one-out cross validation exists.

OK, now, what about k-fold cross-validation. First problem: How do you choose k? Answer: You take a wild guess. I hope I don’t have to explain further.

For the sake of concreteness, assume you magically pick k=5 so that you have 5 subsets of the training data. Next question: Do you create one random partition set of 5 chunks of the data and then use those partitions (4 for training, 1 for testing/evaluation), or do you create different random partitions for each phase of the cross-validation. Answer: If you use one random partition, then if you have a bad selection, your parameter tuning results could be completely incorrect. In other words, you can have no confidence in the generated hyperparameters.

Using one fixed random partition for generalizability metrics is useless because you’ll still need to measure generalizability using a held-out test set. In other words, you can have no confidence in the generated generalizability metric.

Now if you use multiple random partitions, then there is a very strong likelihood (near certainty) that some data items will be used multiple times, and some data items won’t be used at all — so you will have no confidence in the generated generalizability metric.

I like the scikit-learn library a lot, but over time it has bloated out enormously. There are all kinds of modules that have cross-validation integrated — a bad idea. Here’s an example of ElasticNetCV — a particularly egregious example of bad bloat.

OK, so instead of using one random partition, or multiple random partitions, why not use stratified partitioning? Well, that’s another topic but briefly, stratified sampling has a whole host of problems that are just as bad, if not worse, than cross-validation problems. In short, if you use stratified partitions, you end up with hyperparameter or generalizability results with even less confidence.

At this point, while writing this post, I’m mentally exhausted because there are just so many reasons not to use any form of cross-validation, and there are several more, such as multiple problems with the inner-loop-for-hyper-parameter-tuning and outer-loop-for-generalizability-metric. And there are specific technical issues too, such as using cross-validation for learning rate tuning for iterative techniques, especially SGD. OK, I give up trying to explain why something that is so obviously bad is bad.

To summarize: 1.) It’s not even possible to set up cross-validation in a principled way, 2.) Leave-one-out cross-validation makes no sense for parameter tuning or generalizability metrics, 3.) Using k-fold validation produces hyperparameter or generalizability results that you can have absolutely no confidence in.

I get mildly annoyed that it’s even necessary to discuss why cross-validation shouldn’t be used. It’s like explaining why hitting yourself in the face with a brick isn’t a good idea.

I remember when I first was exposed to cross-validation, many years ago. I instantly knew it was bad. So, for year after year, I expected cross-validation to fade away from use. But no, cross-validation has lingered on and on, like lumpy mattresses in the rooms of a zero-star hotel.

Demo program. Replace the “lt” in accuracy() with the Boolean less-than operator.

# elastic_net_cv_scikit.py

import numpy as np
from sklearn.linear_model import ElasticNetCV

np.set_printoptions(precision=4, suppress=True,
  floatmode='fixed', linewidth=60)

# -----------------------------------------------------------

def accuracy(model, data_X, data_y, pct_close):
  n = len(data_X)
  n_correct = 0; n_wrong = 0
  for i in range(n):
    x = data_X[i].reshape(1,-1)
    y = data_y[i]
    y_pred = model.predict(x)[0]

    if np.abs(y - y_pred) "lt" np.abs(y * pct_close):
      n_correct += 1
    else: 
      n_wrong += 1
  return n_correct / (n_correct + n_wrong)

def mse(model, data_X, data_y):
  n = len(data_X)
  sum = 0.0
  for i in range(n):
    actual_y = data_y[i]
    pred_y = model.predict(data_X[i].reshape(1, -1))[0]
    diff = actual_y - pred_y
    sum += diff * diff
  return sum /n

# -----------------------------------------------------------

print("\nBegin elastic net CV regression using scikit ")
print("Note: Not a recommended technique ")

print("\nLoading train (200) and test (40) data ")
train_Xy = np.loadtxt(".\\Data\\synthetic_train_200.txt",
  usecols=[0,1,2,3,4,5], delimiter=",")
train_X = train_Xy[:,[0,1,2,3,4]]
train_y = train_Xy[:,5]

test_Xy = np.loadtxt(".\\Data\\synthetic_test_40.txt",
  usecols=[0,1,2,3,4,5], delimiter=",")
test_X = test_Xy[:,[0,1,2,3,4]]
test_y = test_Xy[:,5]

print("\nFirst three train X: ")
for i in range(3):
  print(train_X[i])
print("\nFirst three train y: ")
for i in range(3):
  print("%0.4f " % train_y[i])

# ElasticNetCV(*, l1_ratio=0.5, eps=0.001,
# n_alphas='deprecated', alphas='warn',
# fit_intercept=True, precompute='auto',
# max_iter=1000, tol=0.0001, cv=None, copy_X=True,
# verbose=0, n_jobs=None, positive=False,
# random_state=None, selection='cyclic')

print("\nCreating elastic-net CV with k=5 ")
n_folds = 5
model = ElasticNetCV(cv=n_folds, random_state=0)
print("Done ")

print("\nTraining model ")
model.fit(train_X, train_y)
print("Done. ")

print("\nModel weights: ")
print(model.coef_)
print("Model bias = %0.4f " % model.intercept_)

print("\nModel alphas examined: ")
print(model.alphas_)
print("Model selected alpha: %0.4f " % model.alpha_)

print("\nEvaluating model ")
acc_train = accuracy(model, train_X, train_y, 0.10)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
print("Accuracy (within 0.10) test = %0.4f " % \
  acc_test)

mse_train = mse(model, train_X, train_y)
mse_test = mse(model, test_X, test_y)
print("\nMSE train = %0.6f " % mse_train)
print("MSE test = %0.6f " % mse_test)

x = train_X[0]
print("\nPredicting for x = ")
print(x)
pred_y = model.predict([x])[0]
print("Predicted y = %0.4f " % pred_y)

print("\nEnd demo ")

Training data:

# synthetic_train_200.txt
#
-0.1660,  0.4406, -0.9998, -0.3953, -0.7065,  0.4840
 0.0776, -0.1616,  0.3704, -0.5911,  0.7562,  0.1568
-0.9452,  0.3409, -0.1654,  0.1174, -0.7192,  0.8054
 0.9365, -0.3732,  0.3846,  0.7528,  0.7892,  0.1345
-0.8299, -0.9219, -0.6603,  0.7563, -0.8033,  0.7955
 0.0663,  0.3838, -0.3690,  0.3730,  0.6693,  0.3206
-0.9634,  0.5003,  0.9777,  0.4963, -0.4391,  0.7377
-0.1042,  0.8172, -0.4128, -0.4244, -0.7399,  0.4801
-0.9613,  0.3577, -0.5767, -0.4689, -0.0169,  0.6861
-0.7065,  0.1786,  0.3995, -0.7953, -0.1719,  0.5569
 0.3888, -0.1716, -0.9001,  0.0718,  0.3276,  0.2500
 0.1731,  0.8068, -0.7251, -0.7214,  0.6148,  0.3297
-0.2046, -0.6693,  0.8550, -0.3045,  0.5016,  0.2129
 0.2473,  0.5019, -0.3022, -0.4601,  0.7918,  0.2613
-0.1438,  0.9297,  0.3269,  0.2434, -0.7705,  0.5171
 0.1568, -0.1837, -0.5259,  0.8068,  0.1474,  0.3307
-0.9943,  0.2343, -0.3467,  0.0541,  0.7719,  0.5581
 0.2467, -0.9684,  0.8589,  0.3818,  0.9946,  0.1092
-0.6553, -0.7257,  0.8652,  0.3936, -0.8680,  0.7018
 0.8460,  0.4230, -0.7515, -0.9602, -0.9476,  0.1996
-0.9434, -0.5076,  0.7201,  0.0777,  0.1056,  0.5664
 0.9392,  0.1221, -0.9627,  0.6013, -0.5341,  0.1533
 0.6142, -0.2243,  0.7271,  0.4942,  0.1125,  0.1661
 0.4260,  0.1194, -0.9749, -0.8561,  0.9346,  0.2230
 0.1362, -0.5934, -0.4953,  0.4877, -0.6091,  0.3810
 0.6937, -0.5203, -0.0125,  0.2399,  0.6580,  0.1460
-0.6864, -0.9628, -0.8600, -0.0273,  0.2127,  0.5387
 0.9772,  0.1595, -0.2397,  0.1019,  0.4907,  0.1611
 0.3385, -0.4702, -0.8673, -0.2598,  0.2594,  0.2270
-0.8669, -0.4794,  0.6095, -0.6131,  0.2789,  0.4700
 0.0493,  0.8496, -0.4734, -0.8681,  0.4701,  0.3516
 0.8639, -0.9721, -0.5313,  0.2336,  0.8980,  0.1412
 0.9004,  0.1133,  0.8312,  0.2831, -0.2200,  0.1782
 0.0991,  0.8524,  0.8375, -0.2102,  0.9265,  0.2150
-0.6521, -0.7473, -0.7298,  0.0113, -0.9570,  0.7422
 0.6190, -0.3105,  0.8802,  0.1640,  0.7577,  0.1056
 0.6895,  0.8108, -0.0802,  0.0927,  0.5972,  0.2214
 0.1982, -0.9689,  0.1870, -0.1326,  0.6147,  0.1310
-0.3695,  0.7858,  0.1557, -0.6320,  0.5759,  0.3773
-0.1596,  0.3581,  0.8372, -0.9992,  0.9535,  0.2071
-0.2468,  0.9476,  0.2094,  0.6577,  0.1494,  0.4132
 0.1737,  0.5000,  0.7166,  0.5102,  0.3961,  0.2611
 0.7290, -0.3546,  0.3416, -0.0983, -0.2358,  0.1332
-0.3652,  0.2438, -0.1395,  0.9476,  0.3556,  0.4170
-0.6029, -0.1466, -0.3133,  0.5953,  0.7600,  0.4334
-0.4596, -0.4953,  0.7098,  0.0554,  0.6043,  0.2775
 0.1450,  0.4663,  0.0380,  0.5418,  0.1377,  0.2931
-0.8636, -0.2442, -0.8407,  0.9656, -0.6368,  0.7429
 0.6237,  0.7499,  0.3768,  0.1390, -0.6781,  0.2185
-0.5499,  0.1850, -0.3755,  0.8326,  0.8193,  0.4399
-0.4858, -0.7782, -0.6141, -0.0008,  0.4572,  0.4197
 0.7033, -0.1683,  0.2334, -0.5327, -0.7961,  0.1776
 0.0317, -0.0457, -0.6947,  0.2436,  0.0880,  0.3345
 0.5031, -0.5559,  0.0387,  0.5706, -0.9553,  0.3107
-0.3513,  0.7458,  0.6894,  0.0769,  0.7332,  0.3170
 0.2205,  0.5992, -0.9309,  0.5405,  0.4635,  0.3532
-0.4806, -0.4859,  0.2646, -0.3094,  0.5932,  0.3202
 0.9809, -0.3995, -0.7140,  0.8026,  0.0831,  0.1600
 0.9495,  0.2732,  0.9878,  0.0921,  0.0529,  0.1289
-0.9476, -0.6792,  0.4913, -0.9392, -0.2669,  0.5966
 0.7247,  0.3854,  0.3819, -0.6227, -0.1162,  0.1550
-0.5922, -0.5045, -0.4757,  0.5003, -0.0860,  0.5863
-0.8861,  0.0170, -0.5761,  0.5972, -0.4053,  0.7301
 0.6877, -0.2380,  0.4997,  0.0223,  0.0819,  0.1404
 0.9189,  0.6079, -0.9354,  0.4188, -0.0700,  0.1907
-0.1428, -0.7820,  0.2676,  0.6059,  0.3936,  0.2790
 0.5324, -0.3151,  0.6917, -0.1425,  0.6480,  0.1071
-0.8432, -0.9633, -0.8666, -0.0828, -0.7733,  0.7784
-0.9444,  0.5097, -0.2103,  0.4939, -0.0952,  0.6787
-0.0520,  0.6063, -0.1952,  0.8094, -0.9259,  0.4836
 0.5477, -0.7487,  0.2370, -0.9793,  0.0773,  0.1241
 0.2450,  0.8116,  0.9799,  0.4222,  0.4636,  0.2355
 0.8186, -0.1983, -0.5003, -0.6531, -0.7611,  0.1511
-0.4714,  0.6382, -0.3788,  0.9648, -0.4667,  0.5950
 0.0673, -0.3711,  0.8215, -0.2669, -0.1328,  0.2677
-0.9381,  0.4338,  0.7820, -0.9454,  0.0441,  0.5518
-0.3480,  0.7190,  0.1170,  0.3805, -0.0943,  0.4724
-0.9813,  0.1535, -0.3771,  0.0345,  0.8328,  0.5438
-0.1471, -0.5052, -0.2574,  0.8637,  0.8737,  0.3042
-0.5454, -0.3712, -0.6505,  0.2142, -0.1728,  0.5783
 0.6327, -0.6297,  0.4038, -0.5193,  0.1484,  0.1153
-0.5424,  0.3282, -0.0055,  0.0380, -0.6506,  0.6613
 0.1414,  0.9935,  0.6337,  0.1887,  0.9520,  0.2540
-0.9351, -0.8128, -0.8693, -0.0965, -0.2491,  0.7353
 0.9507, -0.6640,  0.9456,  0.5349,  0.6485,  0.1059
-0.0462, -0.9737, -0.2940, -0.0159,  0.4602,  0.2606
-0.0627, -0.0852, -0.7247, -0.9782,  0.5166,  0.2977
 0.0478,  0.5098, -0.0723, -0.7504, -0.3750,  0.3335
 0.0090,  0.3477,  0.5403, -0.7393, -0.9542,  0.4415
-0.9748,  0.3449,  0.3736, -0.1015,  0.8296,  0.4358
 0.2887, -0.9895, -0.0311,  0.7186,  0.6608,  0.2057
 0.1570, -0.4518,  0.1211,  0.3435, -0.2951,  0.3244
 0.7117, -0.6099,  0.4946, -0.4208,  0.5476,  0.1096
-0.2929, -0.5726,  0.5346, -0.3827,  0.4665,  0.2465
 0.4889, -0.5572, -0.5718, -0.6021, -0.7150,  0.2163
-0.7782,  0.3491,  0.5996, -0.8389, -0.5366,  0.6516
-0.5847,  0.8347,  0.4226,  0.1078, -0.3910,  0.6134
 0.8469,  0.4121, -0.0439, -0.7476,  0.9521,  0.1571
-0.6803, -0.5948, -0.1376, -0.1916, -0.7065,  0.7156
 0.2878,  0.5086, -0.5785,  0.2019,  0.4979,  0.2980
 0.2764,  0.1943, -0.4090,  0.4632,  0.8906,  0.2960
-0.8877,  0.6705, -0.6155, -0.2098, -0.3998,  0.7107
-0.8398,  0.8093, -0.2597,  0.0614, -0.0118,  0.6502
-0.8476,  0.0158, -0.4769, -0.2859, -0.7839,  0.7715
 0.5751, -0.7868,  0.9714, -0.6457,  0.1448,  0.1175
 0.4802, -0.7001,  0.1022, -0.5668,  0.5184,  0.1090
 0.4458, -0.6469,  0.7239, -0.9604,  0.7205,  0.0779
 0.5175,  0.4339,  0.9747, -0.4438, -0.9924,  0.2879
 0.8678,  0.7158,  0.4577,  0.0334,  0.4139,  0.1678
 0.5406,  0.5012,  0.2264, -0.1963,  0.3946,  0.2088
-0.9938,  0.5498,  0.7928, -0.5214, -0.7585,  0.7687
 0.7661,  0.0863, -0.4266, -0.7233, -0.4197,  0.1466
 0.2277, -0.3517, -0.0853, -0.1118,  0.6563,  0.1767
 0.3499, -0.5570, -0.0655, -0.3705,  0.2537,  0.1632
 0.7547, -0.1046,  0.5689, -0.0861,  0.3125,  0.1257
 0.8186,  0.2110,  0.5335,  0.0094, -0.0039,  0.1391
 0.6858, -0.8644,  0.1465,  0.8855,  0.0357,  0.1845
-0.4967,  0.4015,  0.0805,  0.8977,  0.2487,  0.4663
 0.6760, -0.9841,  0.9787, -0.8446, -0.3557,  0.1509
-0.1203, -0.4885,  0.6054, -0.0443, -0.7313,  0.4854
 0.8557,  0.7919, -0.0169,  0.7134, -0.1628,  0.2002
 0.0115, -0.6209,  0.9300, -0.4116, -0.7931,  0.4052
-0.7114, -0.9718,  0.4319,  0.1290,  0.5892,  0.3661
 0.3915,  0.5557, -0.1870,  0.2955, -0.6404,  0.2954
-0.3564, -0.6548, -0.1827, -0.5172, -0.1862,  0.4622
 0.2392, -0.4959,  0.5857, -0.1341, -0.2850,  0.2470
-0.3394,  0.3947, -0.4627,  0.6166, -0.4094,  0.5325
 0.7107,  0.7768, -0.6312,  0.1707,  0.7964,  0.2757
-0.1078,  0.8437, -0.4420,  0.2177,  0.3649,  0.4028
-0.3139,  0.5595, -0.6505, -0.3161, -0.7108,  0.5546
 0.4335,  0.3986,  0.3770, -0.4932,  0.3847,  0.1810
-0.2562, -0.2894, -0.8847,  0.2633,  0.4146,  0.4036
 0.2272,  0.2966, -0.6601, -0.7011,  0.0284,  0.2778
-0.0743, -0.1421, -0.0054, -0.6770, -0.3151,  0.3597
-0.4762,  0.6891,  0.6007, -0.1467,  0.2140,  0.4266
-0.4061,  0.7193,  0.3432,  0.2669, -0.7505,  0.6147
-0.0588,  0.9731,  0.8966,  0.2902, -0.6966,  0.4955
-0.0627, -0.1439,  0.1985,  0.6999,  0.5022,  0.3077
 0.1587,  0.8494, -0.8705,  0.9827, -0.8940,  0.4263
-0.7850,  0.2473, -0.9040, -0.4308, -0.8779,  0.7199
 0.4070,  0.3369, -0.2428, -0.6236,  0.4940,  0.2215
-0.0242,  0.0513, -0.9430,  0.2885, -0.2987,  0.3947
-0.5416, -0.1322, -0.2351, -0.0604,  0.9590,  0.3683
 0.1055,  0.7783, -0.2901, -0.5090,  0.8220,  0.2984
-0.9129,  0.9015,  0.1128, -0.2473,  0.9901,  0.4776
-0.9378,  0.1424, -0.6391,  0.2619,  0.9618,  0.5368
 0.7498, -0.0963,  0.4169,  0.5549, -0.0103,  0.1614
-0.2612, -0.7156,  0.4538, -0.0460, -0.1022,  0.3717
 0.7720,  0.0552, -0.1818, -0.4622, -0.8560,  0.1685
-0.4177,  0.0070,  0.9319, -0.7812,  0.3461,  0.3052
-0.0001,  0.5542, -0.7128, -0.8336, -0.2016,  0.3803
 0.5356, -0.4194, -0.5662, -0.9666, -0.2027,  0.1776
-0.2378,  0.3187, -0.8582, -0.6948, -0.9668,  0.5474
-0.1947, -0.3579,  0.1158,  0.9869,  0.6690,  0.2992
 0.3992,  0.8365, -0.9205, -0.8593, -0.0520,  0.3154
-0.0209,  0.0793,  0.7905, -0.1067,  0.7541,  0.1864
-0.4928, -0.4524, -0.3433,  0.0951, -0.5597,  0.6261
-0.8118,  0.7404, -0.5263, -0.2280,  0.1431,  0.6349
 0.0516, -0.8480,  0.7483,  0.9023,  0.6250,  0.1959
-0.3212,  0.1093,  0.9488, -0.3766,  0.3376,  0.2735
-0.3481,  0.5490, -0.3484,  0.7797,  0.5034,  0.4379
-0.5785, -0.9170, -0.3563, -0.9258,  0.3877,  0.4121
 0.3407, -0.1391,  0.5356,  0.0720, -0.9203,  0.3458
-0.3287, -0.8954,  0.2102,  0.0241,  0.2349,  0.3247
-0.1353,  0.6954, -0.0919, -0.9692,  0.7461,  0.3338
 0.9036, -0.8982, -0.5299, -0.8733, -0.1567,  0.1187
 0.7277, -0.8368, -0.0538, -0.7489,  0.5458,  0.0830
 0.9049,  0.8878,  0.2279,  0.9470, -0.3103,  0.2194
 0.7957, -0.1308, -0.5284,  0.8817,  0.3684,  0.2172
 0.4647, -0.4931,  0.2010,  0.6292, -0.8918,  0.3371
-0.7390,  0.6849,  0.2367,  0.0626, -0.5034,  0.7039
-0.1567, -0.8711,  0.7940, -0.5932,  0.6525,  0.1710
 0.7635, -0.0265,  0.1969,  0.0545,  0.2496,  0.1445
 0.7675,  0.1354, -0.7698, -0.5460,  0.1920,  0.1728
-0.5211, -0.7372, -0.6763,  0.6897,  0.2044,  0.5217
 0.1913,  0.1980,  0.2314, -0.8816,  0.5006,  0.1998
 0.8964,  0.0694, -0.6149,  0.5059, -0.9854,  0.1825
 0.1767,  0.7104,  0.2093,  0.6452,  0.7590,  0.2832
-0.3580, -0.7541,  0.4426, -0.1193, -0.7465,  0.5657
-0.5996,  0.5766, -0.9758, -0.3933, -0.9572,  0.6800
 0.9950,  0.1641, -0.4132,  0.8579,  0.0142,  0.2003
-0.4717, -0.3894, -0.2567, -0.5111,  0.1691,  0.4266
 0.3917, -0.8561,  0.9422,  0.5061,  0.6123,  0.1212
-0.0366, -0.1087,  0.3449, -0.1025,  0.4086,  0.2475
 0.3633,  0.3943,  0.2372, -0.6980,  0.5216,  0.1925
-0.5325, -0.6466, -0.2178, -0.3589,  0.6310,  0.3568
 0.2271,  0.5200, -0.1447, -0.8011, -0.7699,  0.3128
 0.6415,  0.1993,  0.3777, -0.0178, -0.8237,  0.2181
-0.5298, -0.0768, -0.6028, -0.9490,  0.4588,  0.4356
 0.6870, -0.1431,  0.7294,  0.3141,  0.1621,  0.1632
-0.5985,  0.0591,  0.7889, -0.3900,  0.7419,  0.2945
 0.3661,  0.7984, -0.8486,  0.7572, -0.6183,  0.3449
 0.6995,  0.3342, -0.3113, -0.6972,  0.2707,  0.1712
 0.2565,  0.9126,  0.1798, -0.6043, -0.1413,  0.2893
-0.3265,  0.9839, -0.2395,  0.9854,  0.0376,  0.4770
 0.2690, -0.1722,  0.9818,  0.8599, -0.7015,  0.3954
-0.2102, -0.0768,  0.1219,  0.5607, -0.0256,  0.3949
 0.8216, -0.9555,  0.6422, -0.6231,  0.3715,  0.0801
-0.2896,  0.9484, -0.7545, -0.6249,  0.7789,  0.4370
-0.9985, -0.5448, -0.7092, -0.5931,  0.7926,  0.5402

Test data:

# synthetic_test_40.txt
#
 0.7462,  0.4006, -0.0590,  0.6543, -0.0083,  0.1935
 0.8495, -0.2260, -0.0142, -0.4911,  0.7699,  0.1078
-0.2335, -0.4049,  0.4352, -0.6183, -0.7636,  0.5088
 0.1810, -0.5142,  0.2465,  0.2767, -0.3449,  0.3136
-0.8650,  0.7611, -0.0801,  0.5277, -0.4922,  0.7140
-0.2358, -0.7466, -0.5115, -0.8413, -0.3943,  0.4533
 0.4834,  0.2300,  0.3448, -0.9832,  0.3568,  0.1360
-0.6502, -0.6300,  0.6885,  0.9652,  0.8275,  0.3046
-0.3053,  0.5604,  0.0929,  0.6329, -0.0325,  0.4756
-0.7995,  0.0740, -0.2680,  0.2086,  0.9176,  0.4565
-0.2144, -0.2141,  0.5813,  0.2902, -0.2122,  0.4119
-0.7278, -0.0987, -0.3312, -0.5641,  0.8515,  0.4438
 0.3793,  0.1976,  0.4933,  0.0839,  0.4011,  0.1905
-0.8568,  0.9573, -0.5272,  0.3212, -0.8207,  0.7415
-0.5785,  0.0056, -0.7901, -0.2223,  0.0760,  0.5551
 0.0735, -0.2188,  0.3925,  0.3570,  0.3746,  0.2191
 0.1230, -0.2838,  0.2262,  0.8715,  0.1938,  0.2878
 0.4792, -0.9248,  0.5295,  0.0366, -0.9894,  0.3149
-0.4456,  0.0697,  0.5359, -0.8938,  0.0981,  0.3879
 0.8629, -0.8505, -0.4464,  0.8385,  0.5300,  0.1769
 0.1995,  0.6659,  0.7921,  0.9454,  0.9970,  0.2330
-0.0249, -0.3066, -0.2927, -0.4923,  0.8220,  0.2437
 0.4513, -0.9481, -0.0770, -0.4374, -0.9421,  0.2879
-0.3405,  0.5931, -0.3507, -0.3842,  0.8562,  0.3987
 0.9538,  0.0471,  0.9039,  0.7760,  0.0361,  0.1706
-0.0887,  0.2104,  0.9808,  0.5478, -0.3314,  0.4128
-0.8220, -0.6302,  0.0537, -0.1658,  0.6013,  0.4306
-0.4123, -0.2880,  0.9074, -0.0461, -0.4435,  0.5144
 0.0060,  0.2867, -0.7775,  0.5161,  0.7039,  0.3599
-0.7968, -0.5484,  0.9426, -0.4308,  0.8148,  0.2979
 0.7811,  0.8450, -0.6877,  0.7594,  0.2640,  0.2362
-0.6802, -0.1113, -0.8325, -0.6694, -0.6056,  0.6544
 0.3821,  0.1476,  0.7466, -0.5107,  0.2592,  0.1648
 0.7265,  0.9683, -0.9803, -0.4943, -0.5523,  0.2454
-0.9049, -0.9797, -0.0196, -0.9090, -0.4433,  0.6447
-0.4607,  0.1811, -0.2389,  0.4050, -0.0078,  0.5229
 0.2664, -0.2932, -0.4259, -0.7336,  0.8742,  0.1834
-0.4507,  0.1029, -0.6294, -0.1158, -0.6294,  0.6081
 0.8948, -0.0124,  0.9278,  0.2899, -0.0314,  0.1534
-0.1323, -0.8813, -0.0146, -0.0697,  0.6135,  0.2386

I write code almost every day. Like many skills, writing code is something that must be practiced, and anyway, I enjoy writing code. One evening after work, I figured I’d run the well-known Diabetes Dataset through a support vector regression model. I used the scikit-learn SVR module.

Based on previous experiments with linear regression, quadratic regression, neural network regression, kernel ridge regression, random forest regression, and AdaBoost regression, I was almost certain that the scikit support vector regression model would give poor prediction accuracy — and that’s what happened.

The raw Diabetes Dataset looks like:

59, 2, 32.1, 101.00, 157,  93.2, 38, 4.00, 4.8598, 87, 151
48, 1, 21.6,  87.00, 183, 103.2, 70, 3.00, 3.8918, 69,  75
72, 2, 30.5,  93.00, 156,  93.6, 41, 4.00, 4.6728, 85, 141
. . .

Each line represents a patient. The first 10 values on each line are predictors. The last value on each line is the target value (a diabetes metric) to predict. The predictors are: age, sex, body mass index, blood pressure, serum cholesterol, low-density lipoproteins, high-density lipoproteins, total cholesterol, triglycerides, blood sugar. There are 442 data items.

The sex encoding isn’t explained anywhere but I suspect male = 1, female = 2 because there are 235 1 values and 206 2 values).

Note that this Diabetes Dataset, which is included as an example dataset in the Python language scikit-learn library, is not the same as the Pima Diabetes Dataset from the UCI dataset repository. See https://jamesmccaffreyblog.com/2026/02/03/the-origin-and-history-of-scikit-learn-diabetes-dataset/.

When using SVR, it’s a good idea to normalize predictor values so that a predictor with very large magnitude doesn’t overwhelm the other predictors.

I converted the sex values from 1,2 into 0,1. Then I applied divide-by-constant normalization by dividing the 10 predictor columns by (100, 1, 100, 1000, 1000, 1000, 100, 10, 10, 1000) and the target y values by 1000. The resulting encoded and normalized data looks like:

0.5900, 1.0000, 0.3210, . . . 0.1510
0.4800, 0.0000, 0.2160, . . . 0.0750
0.7200, 1.0000, 0.3050, . . . 0.1410
. . .

I split the 442-items into a 342-item training set and a 100-item test set.

There are two versions of support vector regression. The kernel version is much more powerful than the linear version — so much so that linear SVR is essentially useless. I used kernel SVR.

Support vector regression is closely related to kernel ridge regression (KRR). Both techniques must store training items in memory to make a prediction. But KRR stores all training data, while SVR removes some of the items. On the other hand, SVR does not scale well to large datasets, but KRR can handle arbitrarily large datasets. Briefly, the SVR loss function is not differentiable so a SVR model must be trained with the very ugly quadratic programming technique. KRR can be trained using SGD which can handle any size data.

The output of the scikit SVR demo on the Diabetes Dataset is:

Begin scikit SVR on Diabetes Dataset demo

Loading diabetes train (342), test (100) data
Done

First three X predictors:
[0.5900 1.0000 0.3210 0.1010 0.1570 0.0932 0.3800 0.4000
 0.4860 0.0870]
[0.4800 0.0000 0.2160 0.0870 0.1830 0.1032 0.7000 0.3000
 0.3892 0.0690]
[0.7200 1.0000 0.3050 0.0930 0.1560 0.0936 0.4100 0.4000
 0.4673 0.0850]

First three y targets:
0.1510
0.0750
0.1410

Creating scikit SVR model
Setting gamma = 10.0000
Setting C = 1.0000
Setting epsilon = 0.0100
Done

Training SVR model
Done.

Number support vectors =
298

Evaluating model

Accuracy (within 0.10) train = 0.3538
Accuracy (within 0.10) test = 0.2283

MSE train = 0.0020
MSE test = 0.0034

End demo

These poor results were essentially the same as the results that I got using all other regression techniques.

I have done many experiments with the Diabetes Dataset and I’ve concluded the the default target value in the last column (a patient diabetes score) simply cannot be predicted well. But the variables in columns [4], [5], [6], [7], and [8] can be meaningfully predicted from the other columns.

In some sense, machine learning regression can be thought of as searching for hidden patterns in data.

Left: On the cover of the issue from November 1990, the bunny logo is very difficult to spot. It’s incorporated into the model’s green and white pajama shirt near her right hand. I circled it in red so you don’t go crazy looking for it. Right: On the cover of the February 1991 issue, the bunny logo is disguised to look like one of the red hearts on the model’s shirt (I circled it in blue for you).

Demo program. Replace “lt” (less than) in the accuracy() function with the Boolean less-than operator symbol. (My blog editor chokes on symbols).

# diabetes_scikit_svr.py
# support vector regression for the Diabetes Dataset

import numpy as np
from sklearn.svm import SVR

# SVR(*, kernel='rbf', degree=3, gamma='scale',
# coef0=0.0, tol=0.001, C=1.0, epsilon=0.1, shrinking=True,
# cache_size=200, verbose=False, max_iter=-1)

# -----------------------------------------------------------

np.set_printoptions(precision=4, suppress=True,
  floatmode='fixed', linewidth=60)

# -----------------------------------------------------------

def accuracy(model, data_X, data_y, pct_close):
  n = len(data_X)
  n_correct = 0; n_wrong = 0
  for i in range(n):
    x = data_X[i].reshape(1,-1)
    y = data_y[i]
    y_pred = model.predict(x)[0]

    if np.abs(y - y_pred) "lt" np.abs(y * pct_close):
      n_correct += 1
    else: 
      n_wrong += 1
  return n_correct / (n_correct + n_wrong)

def mse(model, data_X, data_y):
  n = len(data_X)
  sum = 0.0
  for i in range(n):
    actual_y = data_y[i]
    pred_y = model.predict(data_X[i].reshape(1, -1))[0]
    diff = actual_y - pred_y
    sum += diff * diff
  return sum /n

# -----------------------------------------------------------

print("\nBegin scikit SVR on Diabetes Dataset demo ")

print("\nLoading diabetes train (342), test (100) data ")
train_file = ".\\Data\\diabetes_norm_train_342.txt"

cols_X = [0,1,2,3,4,5,6,7,8,9]  
col_y = 10  # cols # 4 5 6 7 8 are much better
train_X = np.loadtxt(train_file, comments="#",
  usecols=cols_X,
  delimiter=",",  dtype=np.float64)
train_y = np.loadtxt(train_file, comments="#", usecols=col_y,
  delimiter=",",  dtype=np.float64)

test_file = ".\\Data\\diabetes_norm_test_100.txt"
test_X = np.loadtxt(test_file, comments="#",
  usecols=cols_X,
  delimiter=",",  dtype=np.float64)
test_y = np.loadtxt(test_file, comments="#", usecols=col_y,
  delimiter=",",  dtype=np.float64)
print("Done ")

# alternative normalization and split
# from sklearn.datasets import load_diabetes
# from sklearn.model_selection import train_test_split
# X, y = load_diabetes(return_X_y=True, scaled=True)
# train_X, test_X, train_y, test_y = \
#   train_test_split(X, y, random_state=0)  # 25% test

print("\nFirst three X predictors: ")
for i in range(3):
  print(train_X[i])
print("\nFirst three y targets: ")
for i in range(3):
  print("%0.4f" % train_y[i])

# grid search
# gamma_vals = [0.01, 0.10, 1.0, 10.0]
# C_vals = [0.01, 0.10, 1.0, 10.0]
# epsilon_vals = [0.01, 0.10, 1.0, 10.0]
# for i in range(len(gamma_vals)):
#   for j in range(len(C_vals)):
#     for k in range(len(epsilon_vals)):
#       print("\n============")
#       print("gamma = %0.4f " % gamma_vals[i])
#       print("C = %0.4f " % C_vals[j])
#       print("epsilon = %0.4f " % epsilon_vals[k])
#       model = SVR(gamma=gamma_vals[i], C=C_vals[j],
#        epsilon=epsilon_vals[k])
#       model.fit(train_X, train_y)
#       acc_train = accuracy(model, train_X, train_y, 0.10)
#       print("Accuracy (within 0.10) train = %0.4f " % \
#        acc_train)
#       acc_test = accuracy(model, test_X, test_y, 0.10)
#       print("Accuracy (within 0.10) test = %0.4f " % \
#        acc_test)
#       mse_train = mse(model, train_X, train_y)
#       mse_test = mse(model, test_X, test_y)
#       print("MSE train = %0.4f " % mse_train)
#       print("MSE test = %0.4f " % mse_test)
#       print("\nNumber support vecs = " + \
#       str(len(model.support_)))
# best result:
# gamma = 10.0000
# C = 1.0000
# epsilon = 0.0100
# Accuracy (within 0.10) train = 0.3538
# Accuracy (within 0.10) test = 0.2283
# MSE train = 0.0020
# MSE test = 0.0034
# Number support vecs = 298

print("\nCreating scikit SVR model ")
gamma = 10.0000  # found by grid search (above)
C = 1.0000
epsilon = 0.0100
print("Setting gamma = %0.4f " % gamma)
print("Setting C = %0.4f " % C)
print("Setting epsilon = %0.4f " % epsilon)
model = SVR(kernel='rbf', gamma=gamma, C=C, epsilon=epsilon)
print("Done ")

print("\nTraining SVR model ")
model.fit(train_X, train_y)
print("Done. ")

# print("\nsupport vectors: ")
# print(model.support_)
print("\nNumber support vectors =  ")
print(len(model.support_))

print("\nEvaluating model ")
acc_train = accuracy(model, train_X, train_y, 0.10)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
print("Accuracy (within 0.10) test = %0.4f " % \
  acc_test)

mse_train = mse(model, train_X, train_y)
mse_test = mse(model, test_X, test_y)
print("\nMSE train = %0.4f " % mse_train)
print("MSE test = %0.4f " % mse_test)

print("\nEnd demo ")

Training data:

# diabetes_norm_train_342.txt
# cols [0] to [9] predictors. col [10] target
# norm division constants:
# 100, -1, 100, 1000, 1000, 1000, 100, 10, 10, 1000, 1000
#
0.5900, 1.0000, 0.3210, 0.1010, 0.1570, 0.0932, 0.3800, 0.4000, 0.4860, 0.0870, 0.1510
0.4800, 0.0000, 0.2160, 0.0870, 0.1830, 0.1032, 0.7000, 0.3000, 0.3892, 0.0690, 0.0750
0.7200, 1.0000, 0.3050, 0.0930, 0.1560, 0.0936, 0.4100, 0.4000, 0.4673, 0.0850, 0.1410
0.2400, 0.0000, 0.2530, 0.0840, 0.1980, 0.1314, 0.4000, 0.5000, 0.4890, 0.0890, 0.2060
0.5000, 0.0000, 0.2300, 0.1010, 0.1920, 0.1254, 0.5200, 0.4000, 0.4291, 0.0800, 0.1350
0.2300, 0.0000, 0.2260, 0.0890, 0.1390, 0.0648, 0.6100, 0.2000, 0.4190, 0.0680, 0.0970
0.3600, 1.0000, 0.2200, 0.0900, 0.1600, 0.0996, 0.5000, 0.3000, 0.3951, 0.0820, 0.1380
0.6600, 1.0000, 0.2620, 0.1140, 0.2550, 0.1850, 0.5600, 0.4550, 0.4249, 0.0920, 0.0630
0.6000, 1.0000, 0.3210, 0.0830, 0.1790, 0.1194, 0.4200, 0.4000, 0.4477, 0.0940, 0.1100
0.2900, 0.0000, 0.3000, 0.0850, 0.1800, 0.0934, 0.4300, 0.4000, 0.5385, 0.0880, 0.3100
0.2200, 0.0000, 0.1860, 0.0970, 0.1140, 0.0576, 0.4600, 0.2000, 0.3951, 0.0830, 0.1010
0.5600, 1.0000, 0.2800, 0.0850, 0.1840, 0.1448, 0.3200, 0.6000, 0.3584, 0.0770, 0.0690
0.5300, 0.0000, 0.2370, 0.0920, 0.1860, 0.1092, 0.6200, 0.3000, 0.4304, 0.0810, 0.1790
0.5000, 1.0000, 0.2620, 0.0970, 0.1860, 0.1054, 0.4900, 0.4000, 0.5063, 0.0880, 0.1850
0.6100, 0.0000, 0.2400, 0.0910, 0.2020, 0.1154, 0.7200, 0.3000, 0.4291, 0.0730, 0.1180
0.3400, 1.0000, 0.2470, 0.1180, 0.2540, 0.1842, 0.3900, 0.7000, 0.5037, 0.0810, 0.1710
0.4700, 0.0000, 0.3030, 0.1090, 0.2070, 0.1002, 0.7000, 0.3000, 0.5215, 0.0980, 0.1660
0.6800, 1.0000, 0.2750, 0.1110, 0.2140, 0.1470, 0.3900, 0.5000, 0.4942, 0.0910, 0.1440
0.3800, 0.0000, 0.2540, 0.0840, 0.1620, 0.1030, 0.4200, 0.4000, 0.4443, 0.0870, 0.0970
0.4100, 0.0000, 0.2470, 0.0830, 0.1870, 0.1082, 0.6000, 0.3000, 0.4543, 0.0780, 0.1680
0.3500, 0.0000, 0.2110, 0.0820, 0.1560, 0.0878, 0.5000, 0.3000, 0.4511, 0.0950, 0.0680
0.2500, 1.0000, 0.2430, 0.0950, 0.1620, 0.0986, 0.5400, 0.3000, 0.3850, 0.0870, 0.0490
0.2500, 0.0000, 0.2600, 0.0920, 0.1870, 0.1204, 0.5600, 0.3000, 0.3970, 0.0880, 0.0680
0.6100, 1.0000, 0.3200, 0.1037, 0.2100, 0.0852, 0.3500, 0.6000, 0.6107, 0.1240, 0.2450
0.3100, 0.0000, 0.2970, 0.0880, 0.1670, 0.1034, 0.4800, 0.4000, 0.4357, 0.0780, 0.1840
0.3000, 1.0000, 0.2520, 0.0830, 0.1780, 0.1184, 0.3400, 0.5000, 0.4852, 0.0830, 0.2020
0.1900, 0.0000, 0.1920, 0.0870, 0.1240, 0.0540, 0.5700, 0.2000, 0.4174, 0.0900, 0.1370
0.4200, 0.0000, 0.3190, 0.0830, 0.1580, 0.0876, 0.5300, 0.3000, 0.4466, 0.1010, 0.0850
0.6300, 0.0000, 0.2440, 0.0730, 0.1600, 0.0914, 0.4800, 0.3000, 0.4635, 0.0780, 0.1310
0.6700, 1.0000, 0.2580, 0.1130, 0.1580, 0.0542, 0.6400, 0.2000, 0.5293, 0.1040, 0.2830
0.3200, 0.0000, 0.3050, 0.0890, 0.1820, 0.1106, 0.5600, 0.3000, 0.4344, 0.0890, 0.1290
0.4200, 0.0000, 0.2030, 0.0710, 0.1610, 0.0812, 0.6600, 0.2000, 0.4234, 0.0810, 0.0590
0.5800, 1.0000, 0.3800, 0.1030, 0.1500, 0.1072, 0.2200, 0.7000, 0.4644, 0.0980, 0.3410
0.5700, 0.0000, 0.2170, 0.0940, 0.1570, 0.0580, 0.8200, 0.2000, 0.4443, 0.0920, 0.0870
0.5300, 0.0000, 0.2050, 0.0780, 0.1470, 0.0842, 0.5200, 0.3000, 0.3989, 0.0750, 0.0650
0.6200, 1.0000, 0.2350, 0.0803, 0.2250, 0.1128, 0.8600, 0.2620, 0.4875, 0.0960, 0.1020
0.5200, 0.0000, 0.2850, 0.1100, 0.1950, 0.0972, 0.6000, 0.3000, 0.5242, 0.0850, 0.2650
0.4600, 0.0000, 0.2740, 0.0780, 0.1710, 0.0880, 0.5800, 0.3000, 0.4828, 0.0900, 0.2760
0.4800, 1.0000, 0.3300, 0.1230, 0.2530, 0.1636, 0.4400, 0.6000, 0.5425, 0.0970, 0.2520
0.4800, 1.0000, 0.2770, 0.0730, 0.1910, 0.1194, 0.4600, 0.4000, 0.4852, 0.0920, 0.0900
0.5000, 1.0000, 0.2560, 0.1010, 0.2290, 0.1622, 0.4300, 0.5000, 0.4779, 0.1140, 0.1000
0.2100, 0.0000, 0.2010, 0.0630, 0.1350, 0.0690, 0.5400, 0.3000, 0.4094, 0.0890, 0.0550
0.3200, 1.0000, 0.2540, 0.0903, 0.1530, 0.1004, 0.3400, 0.4500, 0.4533, 0.0830, 0.0610
0.5400, 0.0000, 0.2420, 0.0740, 0.2040, 0.1090, 0.8200, 0.2000, 0.4174, 0.1090, 0.0920
0.6100, 1.0000, 0.3270, 0.0970, 0.1770, 0.1184, 0.2900, 0.6000, 0.4997, 0.0870, 0.2590
0.5600, 1.0000, 0.2310, 0.1040, 0.1810, 0.1164, 0.4700, 0.4000, 0.4477, 0.0790, 0.0530
0.3300, 0.0000, 0.2530, 0.0850, 0.1550, 0.0850, 0.5100, 0.3000, 0.4554, 0.0700, 0.1900
0.2700, 0.0000, 0.1960, 0.0780, 0.1280, 0.0680, 0.4300, 0.3000, 0.4443, 0.0710, 0.1420
0.6700, 1.0000, 0.2250, 0.0980, 0.1910, 0.1192, 0.6100, 0.3000, 0.3989, 0.0860, 0.0750
0.3700, 1.0000, 0.2770, 0.0930, 0.1800, 0.1194, 0.3000, 0.6000, 0.5030, 0.0880, 0.1420
0.5800, 0.0000, 0.2570, 0.0990, 0.1570, 0.0916, 0.4900, 0.3000, 0.4407, 0.0930, 0.1550
0.6500, 1.0000, 0.2790, 0.1030, 0.1590, 0.0968, 0.4200, 0.4000, 0.4615, 0.0860, 0.2250
0.3400, 0.0000, 0.2550, 0.0930, 0.2180, 0.1440, 0.5700, 0.4000, 0.4443, 0.0880, 0.0590
0.4600, 0.0000, 0.2490, 0.1150, 0.1980, 0.1296, 0.5400, 0.4000, 0.4277, 0.1030, 0.1040
0.3500, 0.0000, 0.2870, 0.0970, 0.2040, 0.1268, 0.6400, 0.3000, 0.4190, 0.0930, 0.1820
0.3700, 0.0000, 0.2180, 0.0840, 0.1840, 0.1010, 0.7300, 0.3000, 0.3912, 0.0930, 0.1280
0.3700, 0.0000, 0.3020, 0.0870, 0.1660, 0.0960, 0.4000, 0.4150, 0.5011, 0.0870, 0.0520
0.4100, 0.0000, 0.2050, 0.0800, 0.1240, 0.0488, 0.6400, 0.2000, 0.4025, 0.0750, 0.0370
0.6000, 0.0000, 0.2040, 0.1050, 0.1980, 0.0784, 0.9900, 0.2000, 0.4635, 0.0790, 0.1700
0.6600, 1.0000, 0.2400, 0.0980, 0.2360, 0.1464, 0.5800, 0.4000, 0.5063, 0.0960, 0.1700
0.2900, 0.0000, 0.2600, 0.0830, 0.1410, 0.0652, 0.6400, 0.2000, 0.4078, 0.0830, 0.0610
0.3700, 1.0000, 0.2680, 0.0790, 0.1570, 0.0980, 0.2800, 0.6000, 0.5043, 0.0960, 0.1440
0.4100, 1.0000, 0.2570, 0.0830, 0.1810, 0.1066, 0.6600, 0.3000, 0.3738, 0.0850, 0.0520
0.3900, 0.0000, 0.2290, 0.0770, 0.2040, 0.1432, 0.4600, 0.4000, 0.4304, 0.0740, 0.1280
0.6700, 1.0000, 0.2400, 0.0830, 0.1430, 0.0772, 0.4900, 0.3000, 0.4431, 0.0940, 0.0710
0.3600, 1.0000, 0.2410, 0.1120, 0.1930, 0.1250, 0.3500, 0.6000, 0.5106, 0.0950, 0.1630
0.4600, 1.0000, 0.2470, 0.0850, 0.1740, 0.1232, 0.3000, 0.6000, 0.4644, 0.0960, 0.1500
0.6000, 1.0000, 0.2500, 0.0897, 0.1850, 0.1208, 0.4600, 0.4020, 0.4511, 0.0920, 0.0970
0.5900, 1.0000, 0.2360, 0.0830, 0.1650, 0.1000, 0.4700, 0.4000, 0.4500, 0.0920, 0.1600
0.5300, 0.0000, 0.2210, 0.0930, 0.1340, 0.0762, 0.4600, 0.3000, 0.4078, 0.0960, 0.1780
0.4800, 0.0000, 0.1990, 0.0910, 0.1890, 0.1096, 0.6900, 0.3000, 0.3951, 0.1010, 0.0480
0.4800, 0.0000, 0.2950, 0.1310, 0.2070, 0.1322, 0.4700, 0.4000, 0.4935, 0.1060, 0.2700
0.6600, 1.0000, 0.2600, 0.0910, 0.2640, 0.1466, 0.6500, 0.4000, 0.5568, 0.0870, 0.2020
0.5200, 1.0000, 0.2450, 0.0940, 0.2170, 0.1494, 0.4800, 0.5000, 0.4585, 0.0890, 0.1110
0.5200, 1.0000, 0.2660, 0.1110, 0.2090, 0.1264, 0.6100, 0.3000, 0.4682, 0.1090, 0.0850
0.4600, 1.0000, 0.2350, 0.0870, 0.1810, 0.1148, 0.4400, 0.4000, 0.4710, 0.0980, 0.0420
0.4000, 1.0000, 0.2900, 0.1150, 0.0970, 0.0472, 0.3500, 0.2770, 0.4304, 0.0950, 0.1700
0.2200, 0.0000, 0.2300, 0.0730, 0.1610, 0.0978, 0.5400, 0.3000, 0.3829, 0.0910, 0.2000
0.5000, 0.0000, 0.2100, 0.0880, 0.1400, 0.0718, 0.3500, 0.4000, 0.5112, 0.0710, 0.2520
0.2000, 0.0000, 0.2290, 0.0870, 0.1910, 0.1282, 0.5300, 0.4000, 0.3892, 0.0850, 0.1130
0.6800, 0.0000, 0.2750, 0.1070, 0.2410, 0.1496, 0.6400, 0.4000, 0.4920, 0.0900, 0.1430
0.5200, 1.0000, 0.2430, 0.0860, 0.1970, 0.1336, 0.4400, 0.5000, 0.4575, 0.0910, 0.0510
0.4400, 0.0000, 0.2310, 0.0870, 0.2130, 0.1264, 0.7700, 0.3000, 0.3871, 0.0720, 0.0520
0.3800, 0.0000, 0.2730, 0.0810, 0.1460, 0.0816, 0.4700, 0.3000, 0.4466, 0.0810, 0.2100
0.4900, 0.0000, 0.2270, 0.0653, 0.1680, 0.0962, 0.6200, 0.2710, 0.3892, 0.0600, 0.0650
0.6100, 0.0000, 0.3300, 0.0950, 0.1820, 0.1148, 0.5400, 0.3000, 0.4190, 0.0740, 0.1410
0.2900, 1.0000, 0.1940, 0.0830, 0.1520, 0.1058, 0.3900, 0.4000, 0.3584, 0.0830, 0.0550
0.6100, 0.0000, 0.2580, 0.0980, 0.2350, 0.1258, 0.7600, 0.3000, 0.5112, 0.0820, 0.1340
0.3400, 1.0000, 0.2260, 0.0750, 0.1660, 0.0918, 0.6000, 0.3000, 0.4263, 0.1080, 0.0420
0.3600, 0.0000, 0.2190, 0.0890, 0.1890, 0.1052, 0.6800, 0.3000, 0.4369, 0.0960, 0.1110
0.5200, 0.0000, 0.2400, 0.0830, 0.1670, 0.0866, 0.7100, 0.2000, 0.3850, 0.0940, 0.0980
0.6100, 0.0000, 0.3120, 0.0790, 0.2350, 0.1568, 0.4700, 0.5000, 0.5050, 0.0960, 0.1640
0.4300, 0.0000, 0.2680, 0.1230, 0.1930, 0.1022, 0.6700, 0.3000, 0.4779, 0.0940, 0.0480
0.3500, 0.0000, 0.2040, 0.0650, 0.1870, 0.1056, 0.6700, 0.2790, 0.4277, 0.0780, 0.0960
0.2700, 0.0000, 0.2480, 0.0910, 0.1890, 0.1068, 0.6900, 0.3000, 0.4190, 0.0690, 0.0900
0.2900, 0.0000, 0.2100, 0.0710, 0.1560, 0.0970, 0.3800, 0.4000, 0.4654, 0.0900, 0.1620
0.6400, 1.0000, 0.2730, 0.1090, 0.1860, 0.1076, 0.3800, 0.5000, 0.5308, 0.0990, 0.1500
0.4100, 0.0000, 0.3460, 0.0873, 0.2050, 0.1426, 0.4100, 0.5000, 0.4673, 0.1100, 0.2790
0.4900, 1.0000, 0.2590, 0.0910, 0.1780, 0.1066, 0.5200, 0.3000, 0.4575, 0.0750, 0.0920
0.4800, 0.0000, 0.2040, 0.0980, 0.2090, 0.1394, 0.4600, 0.5000, 0.4771, 0.0780, 0.0830
0.5300, 0.0000, 0.2800, 0.0880, 0.2330, 0.1438, 0.5800, 0.4000, 0.5050, 0.0910, 0.1280
0.5300, 1.0000, 0.2220, 0.1130, 0.1970, 0.1152, 0.6700, 0.3000, 0.4304, 0.1000, 0.1020
0.2300, 0.0000, 0.2900, 0.0900, 0.2160, 0.1314, 0.6500, 0.3000, 0.4585, 0.0910, 0.3020
0.6500, 1.0000, 0.3020, 0.0980, 0.2190, 0.1606, 0.4000, 0.5000, 0.4522, 0.0840, 0.1980
0.4100, 0.0000, 0.3240, 0.0940, 0.1710, 0.1044, 0.5600, 0.3000, 0.3970, 0.0760, 0.0950
0.5500, 1.0000, 0.2340, 0.0830, 0.1660, 0.1016, 0.4600, 0.4000, 0.4522, 0.0960, 0.0530
0.2200, 0.0000, 0.1930, 0.0820, 0.1560, 0.0932, 0.5200, 0.3000, 0.3989, 0.0710, 0.1340
0.5600, 0.0000, 0.3100, 0.0787, 0.1870, 0.1414, 0.3400, 0.5500, 0.4060, 0.0900, 0.1440
0.5400, 1.0000, 0.3060, 0.1033, 0.1440, 0.0798, 0.3000, 0.4800, 0.5142, 0.1010, 0.2320
0.5900, 1.0000, 0.2550, 0.0953, 0.1900, 0.1394, 0.3500, 0.5430, 0.4357, 0.1170, 0.0810
0.6000, 1.0000, 0.2340, 0.0880, 0.1530, 0.0898, 0.5800, 0.3000, 0.3258, 0.0950, 0.1040
0.5400, 0.0000, 0.2680, 0.0870, 0.2060, 0.1220, 0.6800, 0.3000, 0.4382, 0.0800, 0.0590
0.2500, 0.0000, 0.2830, 0.0870, 0.1930, 0.1280, 0.4900, 0.4000, 0.4382, 0.0920, 0.2460
0.5400, 1.0000, 0.2770, 0.1130, 0.2000, 0.1284, 0.3700, 0.5000, 0.5153, 0.1130, 0.2970
0.5500, 0.0000, 0.3660, 0.1130, 0.1990, 0.0944, 0.4300, 0.4630, 0.5730, 0.0970, 0.2580
0.4000, 1.0000, 0.2650, 0.0930, 0.2360, 0.1470, 0.3700, 0.7000, 0.5561, 0.0920, 0.2290
0.6200, 1.0000, 0.3180, 0.1150, 0.1990, 0.1286, 0.4400, 0.5000, 0.4883, 0.0980, 0.2750
0.6500, 0.0000, 0.2440, 0.1200, 0.2220, 0.1356, 0.3700, 0.6000, 0.5509, 0.1240, 0.2810
0.3300, 1.0000, 0.2540, 0.1020, 0.2060, 0.1410, 0.3900, 0.5000, 0.4868, 0.1050, 0.1790
0.5300, 0.0000, 0.2200, 0.0940, 0.1750, 0.0880, 0.5900, 0.3000, 0.4942, 0.0980, 0.2000
0.3500, 0.0000, 0.2680, 0.0980, 0.1620, 0.1036, 0.4500, 0.4000, 0.4205, 0.0860, 0.2000
0.6600, 0.0000, 0.2800, 0.1010, 0.1950, 0.1292, 0.4000, 0.5000, 0.4860, 0.0940, 0.1730
0.6200, 1.0000, 0.3390, 0.1010, 0.2210, 0.1564, 0.3500, 0.6000, 0.4997, 0.1030, 0.1800
0.5000, 1.0000, 0.2960, 0.0943, 0.3000, 0.2424, 0.3300, 0.9090, 0.4812, 0.1090, 0.0840
0.4700, 0.0000, 0.2860, 0.0970, 0.1640, 0.0906, 0.5600, 0.3000, 0.4466, 0.0880, 0.1210
0.4700, 1.0000, 0.2560, 0.0940, 0.1650, 0.0748, 0.4000, 0.4000, 0.5526, 0.0930, 0.1610
0.2400, 0.0000, 0.2070, 0.0870, 0.1490, 0.0806, 0.6100, 0.2000, 0.3611, 0.0780, 0.0990
0.5800, 1.0000, 0.2620, 0.0910, 0.2170, 0.1242, 0.7100, 0.3000, 0.4691, 0.0680, 0.1090
0.3400, 0.0000, 0.2060, 0.0870, 0.1850, 0.1122, 0.5800, 0.3000, 0.4304, 0.0740, 0.1150
0.5100, 0.0000, 0.2790, 0.0960, 0.1960, 0.1222, 0.4200, 0.5000, 0.5069, 0.1200, 0.2680
0.3100, 1.0000, 0.3530, 0.1250, 0.1870, 0.1124, 0.4800, 0.4000, 0.4890, 0.1090, 0.2740
0.2200, 0.0000, 0.1990, 0.0750, 0.1750, 0.1086, 0.5400, 0.3000, 0.4127, 0.0720, 0.1580
0.5300, 1.0000, 0.2440, 0.0920, 0.2140, 0.1460, 0.5000, 0.4000, 0.4500, 0.0970, 0.1070
0.3700, 1.0000, 0.2140, 0.0830, 0.1280, 0.0696, 0.4900, 0.3000, 0.3850, 0.0840, 0.0830
0.2800, 0.0000, 0.3040, 0.0850, 0.1980, 0.1156, 0.6700, 0.3000, 0.4344, 0.0800, 0.1030
0.4700, 0.0000, 0.3160, 0.0840, 0.1540, 0.0880, 0.3000, 0.5100, 0.5199, 0.1050, 0.2720
0.2300, 0.0000, 0.1880, 0.0780, 0.1450, 0.0720, 0.6300, 0.2000, 0.3912, 0.0860, 0.0850
0.5000, 0.0000, 0.3100, 0.1230, 0.1780, 0.1050, 0.4800, 0.4000, 0.4828, 0.0880, 0.2800
0.5800, 1.0000, 0.3670, 0.1170, 0.1660, 0.0938, 0.4400, 0.4000, 0.4949, 0.1090, 0.3360
0.5500, 0.0000, 0.3210, 0.1100, 0.1640, 0.0842, 0.4200, 0.4000, 0.5242, 0.0900, 0.2810
0.6000, 1.0000, 0.2770, 0.1070, 0.1670, 0.1146, 0.3800, 0.4000, 0.4277, 0.0950, 0.1180
0.4100, 0.0000, 0.3080, 0.0810, 0.2140, 0.1520, 0.2800, 0.7600, 0.5136, 0.1230, 0.3170
0.6000, 1.0000, 0.2750, 0.1060, 0.2290, 0.1438, 0.5100, 0.4000, 0.5142, 0.0910, 0.2350
0.4000, 0.0000, 0.2690, 0.0920, 0.2030, 0.1198, 0.7000, 0.3000, 0.4190, 0.0810, 0.0600
0.5700, 1.0000, 0.3070, 0.0900, 0.2040, 0.1478, 0.3400, 0.6000, 0.4710, 0.0930, 0.1740
0.3700, 0.0000, 0.3830, 0.1130, 0.1650, 0.0946, 0.5300, 0.3000, 0.4466, 0.0790, 0.2590
0.4000, 1.0000, 0.3190, 0.0950, 0.1980, 0.1356, 0.3800, 0.5000, 0.4804, 0.0930, 0.1780
0.3300, 0.0000, 0.3500, 0.0890, 0.2000, 0.1304, 0.4200, 0.4760, 0.4927, 0.1010, 0.1280
0.3200, 1.0000, 0.2780, 0.0890, 0.2160, 0.1462, 0.5500, 0.4000, 0.4304, 0.0910, 0.0960
0.3500, 1.0000, 0.2590, 0.0810, 0.1740, 0.1024, 0.3100, 0.6000, 0.5313, 0.0820, 0.1260
0.5500, 0.0000, 0.3290, 0.1020, 0.1640, 0.1062, 0.4100, 0.4000, 0.4431, 0.0890, 0.2880
0.4900, 0.0000, 0.2600, 0.0930, 0.1830, 0.1002, 0.6400, 0.3000, 0.4543, 0.0880, 0.0880
0.3900, 1.0000, 0.2630, 0.1150, 0.2180, 0.1582, 0.3200, 0.7000, 0.4935, 0.1090, 0.2920
0.6000, 1.0000, 0.2230, 0.1130, 0.1860, 0.1258, 0.4600, 0.4000, 0.4263, 0.0940, 0.0710
0.6700, 1.0000, 0.2830, 0.0930, 0.2040, 0.1322, 0.4900, 0.4000, 0.4736, 0.0920, 0.1970
0.4100, 1.0000, 0.3200, 0.1090, 0.2510, 0.1706, 0.4900, 0.5000, 0.5056, 0.1030, 0.1860
0.4400, 0.0000, 0.2540, 0.0950, 0.1620, 0.0926, 0.5300, 0.3000, 0.4407, 0.0830, 0.0250
0.4800, 1.0000, 0.2330, 0.0893, 0.2120, 0.1428, 0.4600, 0.4610, 0.4754, 0.0980, 0.0840
0.4500, 0.0000, 0.2030, 0.0743, 0.1900, 0.1262, 0.4900, 0.3880, 0.4304, 0.0790, 0.0960
0.4700, 0.0000, 0.3040, 0.1200, 0.1990, 0.1200, 0.4600, 0.4000, 0.5106, 0.0870, 0.1950
0.4600, 0.0000, 0.2060, 0.0730, 0.1720, 0.1070, 0.5100, 0.3000, 0.4249, 0.0800, 0.0530
0.3600, 1.0000, 0.3230, 0.1150, 0.2860, 0.1994, 0.3900, 0.7000, 0.5472, 0.1120, 0.2170
0.3400, 0.0000, 0.2920, 0.0730, 0.1720, 0.1082, 0.4900, 0.4000, 0.4304, 0.0910, 0.1720
0.5300, 1.0000, 0.3310, 0.1170, 0.1830, 0.1190, 0.4800, 0.4000, 0.4382, 0.1060, 0.1310
0.6100, 0.0000, 0.2460, 0.1010, 0.2090, 0.1068, 0.7700, 0.3000, 0.4836, 0.0880, 0.2140
0.3700, 0.0000, 0.2020, 0.0810, 0.1620, 0.0878, 0.6300, 0.3000, 0.4025, 0.0880, 0.0590
0.3300, 1.0000, 0.2080, 0.0840, 0.1250, 0.0702, 0.4600, 0.3000, 0.3784, 0.0660, 0.0700
0.6800, 0.0000, 0.3280, 0.1057, 0.2050, 0.1164, 0.4000, 0.5130, 0.5493, 0.1170, 0.2200
0.4900, 1.0000, 0.3190, 0.0940, 0.2340, 0.1558, 0.3400, 0.7000, 0.5398, 0.1220, 0.2680
0.4800, 0.0000, 0.2390, 0.1090, 0.2320, 0.1052, 0.3700, 0.6000, 0.6107, 0.0960, 0.1520
0.5500, 1.0000, 0.2450, 0.0840, 0.1790, 0.1058, 0.6600, 0.3000, 0.3584, 0.0870, 0.0470
0.4300, 0.0000, 0.2210, 0.0660, 0.1340, 0.0772, 0.4500, 0.3000, 0.4078, 0.0800, 0.0740
0.6000, 1.0000, 0.3300, 0.0970, 0.2170, 0.1256, 0.4500, 0.5000, 0.5447, 0.1120, 0.2950
0.3100, 1.0000, 0.1900, 0.0930, 0.1370, 0.0730, 0.4700, 0.3000, 0.4443, 0.0780, 0.1010
0.5300, 1.0000, 0.2730, 0.0820, 0.1190, 0.0550, 0.3900, 0.3000, 0.4828, 0.0930, 0.1510
0.6700, 0.0000, 0.2280, 0.0870, 0.1660, 0.0986, 0.5200, 0.3000, 0.4344, 0.0920, 0.1270
0.6100, 1.0000, 0.2820, 0.1060, 0.2040, 0.1320, 0.5200, 0.4000, 0.4605, 0.0960, 0.2370
0.6200, 0.0000, 0.2890, 0.0873, 0.2060, 0.1272, 0.3300, 0.6240, 0.5434, 0.0990, 0.2250
0.6000, 0.0000, 0.2560, 0.0870, 0.2070, 0.1258, 0.6900, 0.3000, 0.4111, 0.0840, 0.0810
0.4200, 0.0000, 0.2490, 0.0910, 0.2040, 0.1418, 0.3800, 0.5000, 0.4796, 0.0890, 0.1510
0.3800, 1.0000, 0.2680, 0.1050, 0.1810, 0.1192, 0.3700, 0.5000, 0.4820, 0.0910, 0.1070
0.6200, 0.0000, 0.2240, 0.0790, 0.2220, 0.1474, 0.5900, 0.4000, 0.4357, 0.0760, 0.0640
0.6100, 1.0000, 0.2690, 0.1110, 0.2360, 0.1724, 0.3900, 0.6000, 0.4812, 0.0890, 0.1380
0.6100, 1.0000, 0.2310, 0.1130, 0.1860, 0.1144, 0.4700, 0.4000, 0.4812, 0.1050, 0.1850
0.5300, 0.0000, 0.2860, 0.0880, 0.1710, 0.0988, 0.4100, 0.4000, 0.5050, 0.0990, 0.2650
0.2800, 1.0000, 0.2470, 0.0970, 0.1750, 0.0996, 0.3200, 0.5000, 0.5380, 0.0870, 0.1010
0.2600, 1.0000, 0.3030, 0.0890, 0.2180, 0.1522, 0.3100, 0.7000, 0.5159, 0.0820, 0.1370
0.3000, 0.0000, 0.2130, 0.0870, 0.1340, 0.0630, 0.6300, 0.2000, 0.3689, 0.0660, 0.1430
0.5000, 0.0000, 0.2610, 0.1090, 0.2430, 0.1606, 0.6200, 0.4000, 0.4625, 0.0890, 0.1410
0.4800, 0.0000, 0.2020, 0.0950, 0.1870, 0.1174, 0.5300, 0.4000, 0.4419, 0.0850, 0.0790
0.5100, 0.0000, 0.2520, 0.1030, 0.1760, 0.1122, 0.3700, 0.5000, 0.4898, 0.0900, 0.2920
0.4700, 1.0000, 0.2250, 0.0820, 0.1310, 0.0668, 0.4100, 0.3000, 0.4754, 0.0890, 0.1780
0.6400, 1.0000, 0.2350, 0.0970, 0.2030, 0.1290, 0.5900, 0.3000, 0.4318, 0.0770, 0.0910
0.5100, 1.0000, 0.2590, 0.0760, 0.2400, 0.1690, 0.3900, 0.6000, 0.5075, 0.0960, 0.1160
0.3000, 0.0000, 0.2090, 0.1040, 0.1520, 0.0838, 0.4700, 0.3000, 0.4663, 0.0970, 0.0860
0.5600, 1.0000, 0.2870, 0.0990, 0.2080, 0.1464, 0.3900, 0.5000, 0.4727, 0.0970, 0.1220
0.4200, 0.0000, 0.2210, 0.0850, 0.2130, 0.1386, 0.6000, 0.4000, 0.4277, 0.0940, 0.0720
0.6200, 1.0000, 0.2670, 0.1150, 0.1830, 0.1240, 0.3500, 0.5000, 0.4788, 0.1000, 0.1290
0.3400, 0.0000, 0.3140, 0.0870, 0.1490, 0.0938, 0.4600, 0.3000, 0.3829, 0.0770, 0.1420
0.6000, 0.0000, 0.2220, 0.1047, 0.2210, 0.1054, 0.6000, 0.3680, 0.5628, 0.0930, 0.0900
0.6400, 0.0000, 0.2100, 0.0923, 0.2270, 0.1468, 0.6500, 0.3490, 0.4331, 0.1020, 0.1580
0.3900, 1.0000, 0.2120, 0.0900, 0.1820, 0.1104, 0.6000, 0.3000, 0.4060, 0.0980, 0.0390
0.7100, 1.0000, 0.2650, 0.1050, 0.2810, 0.1736, 0.5500, 0.5000, 0.5568, 0.0840, 0.1960
0.4800, 1.0000, 0.2920, 0.1100, 0.2180, 0.1516, 0.3900, 0.6000, 0.4920, 0.0980, 0.2220
0.7900, 1.0000, 0.2700, 0.1030, 0.1690, 0.1108, 0.3700, 0.5000, 0.4663, 0.1100, 0.2770
0.4000, 0.0000, 0.3070, 0.0990, 0.1770, 0.0854, 0.5000, 0.4000, 0.5338, 0.0850, 0.0990
0.4900, 1.0000, 0.2880, 0.0920, 0.2070, 0.1400, 0.4400, 0.5000, 0.4745, 0.0920, 0.1960
0.5100, 0.0000, 0.3060, 0.1030, 0.1980, 0.1066, 0.5700, 0.3000, 0.5148, 0.1000, 0.2020
0.5700, 0.0000, 0.3010, 0.1170, 0.2020, 0.1396, 0.4200, 0.5000, 0.4625, 0.1200, 0.1550
0.5900, 1.0000, 0.2470, 0.1140, 0.1520, 0.1048, 0.2900, 0.5000, 0.4511, 0.0880, 0.0770
0.5100, 0.0000, 0.2770, 0.0990, 0.2290, 0.1456, 0.6900, 0.3000, 0.4277, 0.0770, 0.1910
0.7400, 0.0000, 0.2980, 0.1010, 0.1710, 0.1048, 0.5000, 0.3000, 0.4394, 0.0860, 0.0700
0.6700, 0.0000, 0.2670, 0.1050, 0.2250, 0.1354, 0.6900, 0.3000, 0.4635, 0.0960, 0.0730
0.4900, 0.0000, 0.1980, 0.0880, 0.1880, 0.1148, 0.5700, 0.3000, 0.4394, 0.0930, 0.0490
0.5700, 0.0000, 0.2330, 0.0880, 0.1550, 0.0636, 0.7800, 0.2000, 0.4205, 0.0780, 0.0650
0.5600, 1.0000, 0.3510, 0.1230, 0.1640, 0.0950, 0.3800, 0.4000, 0.5043, 0.1170, 0.2630
0.5200, 1.0000, 0.2970, 0.1090, 0.2280, 0.1628, 0.3100, 0.8000, 0.5142, 0.1030, 0.2480
0.6900, 0.0000, 0.2930, 0.1240, 0.2230, 0.1390, 0.5400, 0.4000, 0.5011, 0.1020, 0.2960
0.3700, 0.0000, 0.2030, 0.0830, 0.1850, 0.1246, 0.3800, 0.5000, 0.4719, 0.0880, 0.2140
0.2400, 0.0000, 0.2250, 0.0890, 0.1410, 0.0680, 0.5200, 0.3000, 0.4654, 0.0840, 0.1850
0.5500, 1.0000, 0.2270, 0.0930, 0.1540, 0.0942, 0.5300, 0.3000, 0.3526, 0.0750, 0.0780
0.3600, 0.0000, 0.2280, 0.0870, 0.1780, 0.1160, 0.4100, 0.4000, 0.4654, 0.0820, 0.0930
0.4200, 1.0000, 0.2400, 0.1070, 0.1500, 0.0850, 0.4400, 0.3000, 0.4654, 0.0960, 0.2520
0.2100, 0.0000, 0.2420, 0.0760, 0.1470, 0.0770, 0.5300, 0.3000, 0.4443, 0.0790, 0.1500
0.4100, 0.0000, 0.2020, 0.0620, 0.1530, 0.0890, 0.5000, 0.3000, 0.4249, 0.0890, 0.0770
0.5700, 1.0000, 0.2940, 0.1090, 0.1600, 0.0876, 0.3100, 0.5000, 0.5333, 0.0920, 0.2080
0.2000, 1.0000, 0.2210, 0.0870, 0.1710, 0.0996, 0.5800, 0.3000, 0.4205, 0.0780, 0.0770
0.6700, 1.0000, 0.2360, 0.1113, 0.1890, 0.1054, 0.7000, 0.2700, 0.4220, 0.0930, 0.1080
0.3400, 0.0000, 0.2520, 0.0770, 0.1890, 0.1206, 0.5300, 0.4000, 0.4344, 0.0790, 0.1600
0.4100, 1.0000, 0.2490, 0.0860, 0.1920, 0.1150, 0.6100, 0.3000, 0.4382, 0.0940, 0.0530
0.3800, 1.0000, 0.3300, 0.0780, 0.3010, 0.2150, 0.5000, 0.6020, 0.5193, 0.1080, 0.2200
0.5100, 0.0000, 0.2350, 0.1010, 0.1950, 0.1210, 0.5100, 0.4000, 0.4745, 0.0940, 0.1540
0.5200, 1.0000, 0.2640, 0.0913, 0.2180, 0.1520, 0.3900, 0.5590, 0.4905, 0.0990, 0.2590
0.6700, 0.0000, 0.2980, 0.0800, 0.1720, 0.0934, 0.6300, 0.3000, 0.4357, 0.0820, 0.0900
0.6100, 0.0000, 0.3000, 0.1080, 0.1940, 0.1000, 0.5200, 0.3730, 0.5347, 0.1050, 0.2460
0.6700, 1.0000, 0.2500, 0.1117, 0.1460, 0.0934, 0.3300, 0.4420, 0.4585, 0.1030, 0.1240
0.5600, 0.0000, 0.2700, 0.1050, 0.2470, 0.1606, 0.5400, 0.5000, 0.5088, 0.0940, 0.0670
0.6400, 0.0000, 0.2000, 0.0747, 0.1890, 0.1148, 0.6200, 0.3050, 0.4111, 0.0910, 0.0720
0.5800, 1.0000, 0.2550, 0.1120, 0.1630, 0.1106, 0.2900, 0.6000, 0.4762, 0.0860, 0.2570
0.5500, 0.0000, 0.2820, 0.0910, 0.2500, 0.1402, 0.6700, 0.4000, 0.5366, 0.1030, 0.2620
0.6200, 1.0000, 0.3330, 0.1140, 0.1820, 0.1140, 0.3800, 0.5000, 0.5011, 0.0960, 0.2750
0.5700, 1.0000, 0.2560, 0.0960, 0.2000, 0.1330, 0.5200, 0.3850, 0.4318, 0.1050, 0.1770
0.2000, 1.0000, 0.2420, 0.0880, 0.1260, 0.0722, 0.4500, 0.3000, 0.3784, 0.0740, 0.0710
0.5300, 1.0000, 0.2210, 0.0980, 0.1650, 0.1052, 0.4700, 0.4000, 0.4159, 0.0810, 0.0470
0.3200, 1.0000, 0.3140, 0.0890, 0.1530, 0.0842, 0.5600, 0.3000, 0.4159, 0.0900, 0.1870
0.4100, 0.0000, 0.2310, 0.0860, 0.1480, 0.0780, 0.5800, 0.3000, 0.4094, 0.0600, 0.1250
0.6000, 0.0000, 0.2340, 0.0767, 0.2470, 0.1480, 0.6500, 0.3800, 0.5136, 0.0770, 0.0780
0.2600, 0.0000, 0.1880, 0.0830, 0.1910, 0.1036, 0.6900, 0.3000, 0.4522, 0.0690, 0.0510
0.3700, 0.0000, 0.3080, 0.1120, 0.2820, 0.1972, 0.4300, 0.7000, 0.5342, 0.1010, 0.2580
0.4500, 0.0000, 0.3200, 0.1100, 0.2240, 0.1342, 0.4500, 0.5000, 0.5412, 0.0930, 0.2150
0.6700, 0.0000, 0.3160, 0.1160, 0.1790, 0.0904, 0.4100, 0.4000, 0.5472, 0.1000, 0.3030
0.3400, 1.0000, 0.3550, 0.1200, 0.2330, 0.1466, 0.3400, 0.7000, 0.5568, 0.1010, 0.2430
0.5000, 0.0000, 0.3190, 0.0783, 0.2070, 0.1492, 0.3800, 0.5450, 0.4595, 0.0840, 0.0910
0.7100, 0.0000, 0.2950, 0.0970, 0.2270, 0.1516, 0.4500, 0.5000, 0.5024, 0.1080, 0.1500
0.5700, 1.0000, 0.3160, 0.1170, 0.2250, 0.1076, 0.4000, 0.6000, 0.5958, 0.1130, 0.3100
0.4900, 0.0000, 0.2030, 0.0930, 0.1840, 0.1030, 0.6100, 0.3000, 0.4605, 0.0930, 0.1530
0.3500, 0.0000, 0.4130, 0.0810, 0.1680, 0.1028, 0.3700, 0.5000, 0.4949, 0.0940, 0.3460
0.4100, 1.0000, 0.2120, 0.1020, 0.1840, 0.1004, 0.6400, 0.3000, 0.4585, 0.0790, 0.0630
0.7000, 1.0000, 0.2410, 0.0823, 0.1940, 0.1492, 0.3100, 0.6260, 0.4234, 0.1050, 0.0890
0.5200, 0.0000, 0.2300, 0.1070, 0.1790, 0.1237, 0.4250, 0.4210, 0.4159, 0.0930, 0.0500
0.6000, 0.0000, 0.2560, 0.0780, 0.1950, 0.0954, 0.9100, 0.2000, 0.3761, 0.0870, 0.0390
0.6200, 0.0000, 0.2250, 0.1250, 0.2150, 0.0990, 0.9800, 0.2000, 0.4500, 0.0950, 0.1030
0.4400, 1.0000, 0.3820, 0.1230, 0.2010, 0.1266, 0.4400, 0.5000, 0.5024, 0.0920, 0.3080
0.2800, 1.0000, 0.1920, 0.0810, 0.1550, 0.0946, 0.5100, 0.3000, 0.3850, 0.0870, 0.1160
0.5800, 1.0000, 0.2900, 0.0850, 0.1560, 0.1092, 0.3600, 0.4000, 0.3989, 0.0860, 0.1450
0.3900, 1.0000, 0.2400, 0.0897, 0.1900, 0.1136, 0.5200, 0.3650, 0.4804, 0.1010, 0.0740
0.3400, 1.0000, 0.2060, 0.0980, 0.1830, 0.0920, 0.8300, 0.2000, 0.3689, 0.0920, 0.0450
0.6500, 0.0000, 0.2630, 0.0700, 0.2440, 0.1662, 0.5100, 0.5000, 0.4898, 0.0980, 0.1150
0.6600, 1.0000, 0.3460, 0.1150, 0.2040, 0.1394, 0.3600, 0.6000, 0.4963, 0.1090, 0.2640
0.5100, 0.0000, 0.2340, 0.0870, 0.2200, 0.1088, 0.9300, 0.2000, 0.4511, 0.0820, 0.0870
0.5000, 1.0000, 0.2920, 0.1190, 0.1620, 0.0852, 0.5400, 0.3000, 0.4736, 0.0950, 0.2020
0.5900, 1.0000, 0.2720, 0.1070, 0.1580, 0.1020, 0.3900, 0.4000, 0.4443, 0.0930, 0.1270
0.5200, 0.0000, 0.2700, 0.0783, 0.1340, 0.0730, 0.4400, 0.3050, 0.4443, 0.0690, 0.1820
0.6900, 1.0000, 0.2450, 0.1080, 0.2430, 0.1364, 0.4000, 0.6000, 0.5808, 0.1000, 0.2410
0.5300, 0.0000, 0.2410, 0.1050, 0.1840, 0.1134, 0.4600, 0.4000, 0.4812, 0.0950, 0.0660
0.4700, 1.0000, 0.2530, 0.0980, 0.1730, 0.1056, 0.4400, 0.4000, 0.4762, 0.1080, 0.0940
0.5200, 0.0000, 0.2880, 0.1130, 0.2800, 0.1740, 0.6700, 0.4000, 0.5273, 0.0860, 0.2830
0.3900, 0.0000, 0.2090, 0.0950, 0.1500, 0.0656, 0.6800, 0.2000, 0.4407, 0.0950, 0.0640
0.6700, 1.0000, 0.2300, 0.0700, 0.1840, 0.1280, 0.3500, 0.5000, 0.4654, 0.0990, 0.1020
0.5900, 1.0000, 0.2410, 0.0960, 0.1700, 0.0986, 0.5400, 0.3000, 0.4466, 0.0850, 0.2000
0.5100, 1.0000, 0.2810, 0.1060, 0.2020, 0.1222, 0.5500, 0.4000, 0.4820, 0.0870, 0.2650
0.2300, 1.0000, 0.1800, 0.0780, 0.1710, 0.0960, 0.4800, 0.4000, 0.4905, 0.0920, 0.0940
0.6800, 0.0000, 0.2590, 0.0930, 0.2530, 0.1812, 0.5300, 0.5000, 0.4543, 0.0980, 0.2300
0.4400, 0.0000, 0.2150, 0.0850, 0.1570, 0.0922, 0.5500, 0.3000, 0.3892, 0.0840, 0.1810
0.6000, 1.0000, 0.2430, 0.1030, 0.1410, 0.0866, 0.3300, 0.4000, 0.4673, 0.0780, 0.1560
0.5200, 0.0000, 0.2450, 0.0900, 0.1980, 0.1290, 0.2900, 0.7000, 0.5298, 0.0860, 0.2330
0.3800, 0.0000, 0.2130, 0.0720, 0.1650, 0.0602, 0.8800, 0.2000, 0.4431, 0.0900, 0.0600
0.6100, 0.0000, 0.2580, 0.0900, 0.2800, 0.1954, 0.5500, 0.5000, 0.4997, 0.0900, 0.2190
0.6800, 1.0000, 0.2480, 0.1010, 0.2210, 0.1514, 0.6000, 0.4000, 0.3871, 0.0870, 0.0800
0.2800, 1.0000, 0.3150, 0.0830, 0.2280, 0.1494, 0.3800, 0.6000, 0.5313, 0.0830, 0.0680
0.6500, 1.0000, 0.3350, 0.1020, 0.1900, 0.1262, 0.3500, 0.5000, 0.4970, 0.1020, 0.3320
0.6900, 0.0000, 0.2810, 0.1130, 0.2340, 0.1428, 0.5200, 0.4000, 0.5278, 0.0770, 0.2480
0.5100, 0.0000, 0.2430, 0.0853, 0.1530, 0.0716, 0.7100, 0.2150, 0.3951, 0.0820, 0.0840
0.2900, 0.0000, 0.3500, 0.0983, 0.2040, 0.1426, 0.5000, 0.4080, 0.4043, 0.0910, 0.2000
0.5500, 1.0000, 0.2350, 0.0930, 0.1770, 0.1268, 0.4100, 0.4000, 0.3829, 0.0830, 0.0550
0.3400, 1.0000, 0.3000, 0.0830, 0.1850, 0.1072, 0.5300, 0.3000, 0.4820, 0.0920, 0.0850
0.6700, 0.0000, 0.2070, 0.0830, 0.1700, 0.0998, 0.5900, 0.3000, 0.4025, 0.0770, 0.0890
0.4900, 0.0000, 0.2560, 0.0760, 0.1610, 0.0998, 0.5100, 0.3000, 0.3932, 0.0780, 0.0310
0.5500, 1.0000, 0.2290, 0.0810, 0.1230, 0.0672, 0.4100, 0.3000, 0.4304, 0.0880, 0.1290
0.5900, 1.0000, 0.2510, 0.0900, 0.1630, 0.1014, 0.4600, 0.4000, 0.4357, 0.0910, 0.0830
0.5300, 0.0000, 0.3320, 0.0827, 0.1860, 0.1068, 0.4600, 0.4040, 0.5112, 0.1020, 0.2750
0.4800, 1.0000, 0.2410, 0.1100, 0.2090, 0.1346, 0.5800, 0.4000, 0.4407, 0.1000, 0.0650
0.5200, 0.0000, 0.2950, 0.1043, 0.2110, 0.1328, 0.4900, 0.4310, 0.4984, 0.0980, 0.1980
0.6900, 0.0000, 0.2960, 0.1220, 0.2310, 0.1284, 0.5600, 0.4000, 0.5451, 0.0860, 0.2360
0.6000, 1.0000, 0.2280, 0.1100, 0.2450, 0.1898, 0.3900, 0.6000, 0.4394, 0.0880, 0.2530
0.4600, 1.0000, 0.2270, 0.0830, 0.1830, 0.1258, 0.3200, 0.6000, 0.4836, 0.0750, 0.1240
0.5100, 1.0000, 0.2620, 0.1010, 0.1610, 0.0996, 0.4800, 0.3000, 0.4205, 0.0880, 0.0440
0.6700, 1.0000, 0.2350, 0.0960, 0.2070, 0.1382, 0.4200, 0.5000, 0.4898, 0.1110, 0.1720
0.4900, 0.0000, 0.2210, 0.0850, 0.1360, 0.0634, 0.6200, 0.2190, 0.3970, 0.0720, 0.1140
0.4600, 1.0000, 0.2650, 0.0940, 0.2470, 0.1602, 0.5900, 0.4000, 0.4935, 0.1110, 0.1420
0.4700, 0.0000, 0.3240, 0.1050, 0.1880, 0.1250, 0.4600, 0.4090, 0.4443, 0.0990, 0.1090
0.7500, 0.0000, 0.3010, 0.0780, 0.2220, 0.1542, 0.4400, 0.5050, 0.4779, 0.0970, 0.1800
0.2800, 0.0000, 0.2420, 0.0930, 0.1740, 0.1064, 0.5400, 0.3000, 0.4220, 0.0840, 0.1440
0.6500, 1.0000, 0.3130, 0.1100, 0.2130, 0.1280, 0.4700, 0.5000, 0.5247, 0.0910, 0.1630
0.4200, 0.0000, 0.3010, 0.0910, 0.1820, 0.1148, 0.4900, 0.4000, 0.4511, 0.0820, 0.1470
0.5100, 0.0000, 0.2450, 0.0790, 0.2120, 0.1286, 0.6500, 0.3000, 0.4522, 0.0910, 0.0970
0.5300, 1.0000, 0.2770, 0.0950, 0.1900, 0.1018, 0.4100, 0.5000, 0.5464, 0.1010, 0.2200
0.5400, 0.0000, 0.2320, 0.1107, 0.2380, 0.1628, 0.4800, 0.4960, 0.4913, 0.1080, 0.1900
0.7300, 0.0000, 0.2700, 0.1020, 0.2110, 0.1210, 0.6700, 0.3000, 0.4745, 0.0990, 0.1090
0.5400, 0.0000, 0.2680, 0.1080, 0.1760, 0.0806, 0.6700, 0.3000, 0.4956, 0.1060, 0.1910
0.4200, 0.0000, 0.2920, 0.0930, 0.2490, 0.1742, 0.4500, 0.6000, 0.5004, 0.0920, 0.1220
0.7500, 0.0000, 0.3120, 0.1177, 0.2290, 0.1388, 0.2900, 0.7900, 0.5724, 0.1060, 0.2300
0.5500, 1.0000, 0.3210, 0.1127, 0.2070, 0.0924, 0.2500, 0.8280, 0.6105, 0.1110, 0.2420
0.6800, 1.0000, 0.2570, 0.1090, 0.2330, 0.1126, 0.3500, 0.7000, 0.6057, 0.1050, 0.2480
0.5700, 0.0000, 0.2690, 0.0980, 0.2460, 0.1652, 0.3800, 0.7000, 0.5366, 0.0960, 0.2490
0.4800, 0.0000, 0.3140, 0.0753, 0.2420, 0.1516, 0.3800, 0.6370, 0.5568, 0.1030, 0.1920
0.6100, 1.0000, 0.2560, 0.0850, 0.1840, 0.1162, 0.3900, 0.5000, 0.4970, 0.0980, 0.1310
0.6900, 0.0000, 0.3700, 0.1030, 0.2070, 0.1314, 0.5500, 0.4000, 0.4635, 0.0900, 0.2370
0.3800, 0.0000, 0.3260, 0.0770, 0.1680, 0.1006, 0.4700, 0.4000, 0.4625, 0.0960, 0.0780
0.4500, 1.0000, 0.2120, 0.0940, 0.1690, 0.0968, 0.5500, 0.3000, 0.4454, 0.1020, 0.1350
0.5100, 1.0000, 0.2920, 0.1070, 0.1870, 0.1390, 0.3200, 0.6000, 0.4382, 0.0950, 0.2440
0.7100, 1.0000, 0.2400, 0.0840, 0.1380, 0.0858, 0.3900, 0.4000, 0.4190, 0.0900, 0.1990
0.5700, 0.0000, 0.3610, 0.1170, 0.1810, 0.1082, 0.3400, 0.5000, 0.5268, 0.1000, 0.2700
0.5600, 1.0000, 0.2580, 0.1030, 0.1770, 0.1144, 0.3400, 0.5000, 0.4963, 0.0990, 0.1640
0.3200, 1.0000, 0.2200, 0.0880, 0.1370, 0.0786, 0.4800, 0.3000, 0.3951, 0.0780, 0.0720
0.5000, 0.0000, 0.2190, 0.0910, 0.1900, 0.1112, 0.6700, 0.3000, 0.4078, 0.0770, 0.0960
0.4300, 0.0000, 0.3430, 0.0840, 0.2560, 0.1726, 0.3300, 0.8000, 0.5529, 0.1040, 0.3060
0.5400, 1.0000, 0.2520, 0.1150, 0.1810, 0.1200, 0.3900, 0.5000, 0.4701, 0.0920, 0.0910
0.3100, 0.0000, 0.2330, 0.0850, 0.1900, 0.1308, 0.4300, 0.4000, 0.4394, 0.0770, 0.2140
0.5600, 0.0000, 0.2570, 0.0800, 0.2440, 0.1516, 0.5900, 0.4000, 0.5118, 0.0950, 0.0950
0.4400, 0.0000, 0.2510, 0.1330, 0.1820, 0.1130, 0.5500, 0.3000, 0.4249, 0.0840, 0.2160
0.5700, 1.0000, 0.3190, 0.1110, 0.1730, 0.1162, 0.4100, 0.4000, 0.4369, 0.0870, 0.2630

Test data:

# diabetes_norm_test_100.txt
#
0.6400, 1.0000, 0.2840, 0.1110, 0.1840, 0.1270, 0.4100, 0.4000, 0.4382, 0.0970, 0.1780
0.4300, 0.0000, 0.2810, 0.1210, 0.1920, 0.1210, 0.6000, 0.3000, 0.4007, 0.0930, 0.1130
0.1900, 0.0000, 0.2530, 0.0830, 0.2250, 0.1566, 0.4600, 0.5000, 0.4719, 0.0840, 0.2000
0.7100, 1.0000, 0.2610, 0.0850, 0.2200, 0.1524, 0.4700, 0.5000, 0.4635, 0.0910, 0.1390
0.5000, 1.0000, 0.2800, 0.1040, 0.2820, 0.1968, 0.4400, 0.6000, 0.5328, 0.0950, 0.1390
0.5900, 1.0000, 0.2360, 0.0730, 0.1800, 0.1074, 0.5100, 0.4000, 0.4682, 0.0840, 0.0880
0.5700, 0.0000, 0.2450, 0.0930, 0.1860, 0.0966, 0.7100, 0.3000, 0.4522, 0.0910, 0.1480
0.4900, 1.0000, 0.2100, 0.0820, 0.1190, 0.0854, 0.2300, 0.5000, 0.3970, 0.0740, 0.0880
0.4100, 1.0000, 0.3200, 0.1260, 0.1980, 0.1042, 0.4900, 0.4000, 0.5412, 0.1240, 0.2430
0.2500, 1.0000, 0.2260, 0.0850, 0.1300, 0.0710, 0.4800, 0.3000, 0.4007, 0.0810, 0.0710
0.5200, 1.0000, 0.1970, 0.0810, 0.1520, 0.0534, 0.8200, 0.2000, 0.4419, 0.0820, 0.0770
0.3400, 0.0000, 0.2120, 0.0840, 0.2540, 0.1134, 0.5200, 0.5000, 0.6094, 0.0920, 0.1090
0.4200, 1.0000, 0.3060, 0.1010, 0.2690, 0.1722, 0.5000, 0.5000, 0.5455, 0.1060, 0.2720
0.2800, 1.0000, 0.2550, 0.0990, 0.1620, 0.1016, 0.4600, 0.4000, 0.4277, 0.0940, 0.0600
0.4700, 1.0000, 0.2330, 0.0900, 0.1950, 0.1258, 0.5400, 0.4000, 0.4331, 0.0730, 0.0540
0.3200, 1.0000, 0.3100, 0.1000, 0.1770, 0.0962, 0.4500, 0.4000, 0.5187, 0.0770, 0.2210
0.4300, 0.0000, 0.1850, 0.0870, 0.1630, 0.0936, 0.6100, 0.2670, 0.3738, 0.0800, 0.0900
0.5900, 1.0000, 0.2690, 0.1040, 0.1940, 0.1266, 0.4300, 0.5000, 0.4804, 0.1060, 0.3110
0.5300, 0.0000, 0.2830, 0.1010, 0.1790, 0.1070, 0.4800, 0.4000, 0.4788, 0.1010, 0.2810
0.6000, 0.0000, 0.2570, 0.1030, 0.1580, 0.0846, 0.6400, 0.2000, 0.3850, 0.0970, 0.1820
0.5400, 1.0000, 0.3610, 0.1150, 0.1630, 0.0984, 0.4300, 0.4000, 0.4682, 0.1010, 0.3210
0.3500, 1.0000, 0.2410, 0.0947, 0.1550, 0.0974, 0.3200, 0.4840, 0.4852, 0.0940, 0.0580
0.4900, 1.0000, 0.2580, 0.0890, 0.1820, 0.1186, 0.3900, 0.5000, 0.4804, 0.1150, 0.2620
0.5800, 0.0000, 0.2280, 0.0910, 0.1960, 0.1188, 0.4800, 0.4000, 0.4984, 0.1150, 0.2060
0.3600, 1.0000, 0.3910, 0.0900, 0.2190, 0.1358, 0.3800, 0.6000, 0.5421, 0.1030, 0.2330
0.4600, 1.0000, 0.4220, 0.0990, 0.2110, 0.1370, 0.4400, 0.5000, 0.5011, 0.0990, 0.2420
0.4400, 1.0000, 0.2660, 0.0990, 0.2050, 0.1090, 0.4300, 0.5000, 0.5580, 0.1110, 0.1230
0.4600, 0.0000, 0.2990, 0.0830, 0.1710, 0.1130, 0.3800, 0.4500, 0.4585, 0.0980, 0.1670
0.5400, 0.0000, 0.2100, 0.0780, 0.1880, 0.1074, 0.7000, 0.3000, 0.3970, 0.0730, 0.0630
0.6300, 1.0000, 0.2550, 0.1090, 0.2260, 0.1032, 0.4600, 0.5000, 0.5951, 0.0870, 0.1970
0.4100, 1.0000, 0.2420, 0.0900, 0.1990, 0.1236, 0.5700, 0.4000, 0.4522, 0.0860, 0.0710
0.2800, 0.0000, 0.2540, 0.0930, 0.1410, 0.0790, 0.4900, 0.3000, 0.4174, 0.0910, 0.1680
0.1900, 0.0000, 0.2320, 0.0750, 0.1430, 0.0704, 0.5200, 0.3000, 0.4635, 0.0720, 0.1400
0.6100, 1.0000, 0.2610, 0.1260, 0.2150, 0.1298, 0.5700, 0.4000, 0.4949, 0.0960, 0.2170
0.4800, 0.0000, 0.3270, 0.0930, 0.2760, 0.1986, 0.4300, 0.6420, 0.5148, 0.0910, 0.1210
0.5400, 1.0000, 0.2730, 0.1000, 0.2000, 0.1440, 0.3300, 0.6000, 0.4745, 0.0760, 0.2350
0.5300, 1.0000, 0.2660, 0.0930, 0.1850, 0.1224, 0.3600, 0.5000, 0.4890, 0.0820, 0.2450
0.4800, 0.0000, 0.2280, 0.1010, 0.1100, 0.0416, 0.5600, 0.2000, 0.4127, 0.0970, 0.0400
0.5300, 0.0000, 0.2880, 0.1117, 0.1450, 0.0872, 0.4600, 0.3150, 0.4078, 0.0850, 0.0520
0.2900, 1.0000, 0.1810, 0.0730, 0.1580, 0.0990, 0.4100, 0.4000, 0.4500, 0.0780, 0.1040
0.6200, 0.0000, 0.3200, 0.0880, 0.1720, 0.0690, 0.3800, 0.4000, 0.5784, 0.1000, 0.1320
0.5000, 1.0000, 0.2370, 0.0920, 0.1660, 0.0970, 0.5200, 0.3000, 0.4443, 0.0930, 0.0880
0.5800, 1.0000, 0.2360, 0.0960, 0.2570, 0.1710, 0.5900, 0.4000, 0.4905, 0.0820, 0.0690
0.5500, 1.0000, 0.2460, 0.1090, 0.1430, 0.0764, 0.5100, 0.3000, 0.4357, 0.0880, 0.2190
0.5400, 0.0000, 0.2260, 0.0900, 0.1830, 0.1042, 0.6400, 0.3000, 0.4304, 0.0920, 0.0720
0.3600, 0.0000, 0.2780, 0.0730, 0.1530, 0.1044, 0.4200, 0.4000, 0.3497, 0.0730, 0.2010
0.6300, 1.0000, 0.2410, 0.1110, 0.1840, 0.1122, 0.4400, 0.4000, 0.4935, 0.0820, 0.1100
0.4700, 1.0000, 0.2650, 0.0700, 0.1810, 0.1048, 0.6300, 0.3000, 0.4190, 0.0700, 0.0510
0.5100, 1.0000, 0.3280, 0.1120, 0.2020, 0.1006, 0.3700, 0.5000, 0.5775, 0.1090, 0.2770
0.4200, 0.0000, 0.1990, 0.0760, 0.1460, 0.0832, 0.5500, 0.3000, 0.3664, 0.0790, 0.0630
0.3700, 1.0000, 0.2360, 0.0940, 0.2050, 0.1388, 0.5300, 0.4000, 0.4190, 0.1070, 0.1180
0.2800, 0.0000, 0.2210, 0.0820, 0.1680, 0.1006, 0.5400, 0.3000, 0.4205, 0.0860, 0.0690
0.5800, 0.0000, 0.2810, 0.1110, 0.1980, 0.0806, 0.3100, 0.6000, 0.6068, 0.0930, 0.2730
0.3200, 0.0000, 0.2650, 0.0860, 0.1840, 0.1016, 0.5300, 0.4000, 0.4990, 0.0780, 0.2580
0.2500, 1.0000, 0.2350, 0.0880, 0.1430, 0.0808, 0.5500, 0.3000, 0.3584, 0.0830, 0.0430
0.6300, 0.0000, 0.2600, 0.0857, 0.1550, 0.0782, 0.4600, 0.3370, 0.5037, 0.0970, 0.1980
0.5200, 0.0000, 0.2780, 0.0850, 0.2190, 0.1360, 0.4900, 0.4000, 0.5136, 0.0750, 0.2420
0.6500, 1.0000, 0.2850, 0.1090, 0.2010, 0.1230, 0.4600, 0.4000, 0.5075, 0.0960, 0.2320
0.4200, 0.0000, 0.3060, 0.1210, 0.1760, 0.0928, 0.6900, 0.3000, 0.4263, 0.0890, 0.1750
0.5300, 0.0000, 0.2220, 0.0780, 0.1640, 0.0810, 0.7000, 0.2000, 0.4174, 0.1010, 0.0930
0.7900, 1.0000, 0.2330, 0.0880, 0.1860, 0.1284, 0.3300, 0.6000, 0.4812, 0.1020, 0.1680
0.4300, 0.0000, 0.3540, 0.0930, 0.1850, 0.1002, 0.4400, 0.4000, 0.5318, 0.1010, 0.2750
0.4400, 0.0000, 0.3140, 0.1150, 0.1650, 0.0976, 0.5200, 0.3000, 0.4344, 0.0890, 0.2930
0.6200, 1.0000, 0.3780, 0.1190, 0.1130, 0.0510, 0.3100, 0.4000, 0.5043, 0.0840, 0.2810
0.3300, 0.0000, 0.1890, 0.0700, 0.1620, 0.0918, 0.5900, 0.3000, 0.4025, 0.0580, 0.0720
0.5600, 0.0000, 0.3500, 0.0793, 0.1950, 0.1408, 0.4200, 0.4640, 0.4111, 0.0960, 0.1400
0.6600, 0.0000, 0.2170, 0.1260, 0.2120, 0.1278, 0.4500, 0.4710, 0.5278, 0.1010, 0.1890
0.3400, 1.0000, 0.2530, 0.1110, 0.2300, 0.1620, 0.3900, 0.6000, 0.4977, 0.0900, 0.1810
0.4600, 1.0000, 0.2380, 0.0970, 0.2240, 0.1392, 0.4200, 0.5000, 0.5366, 0.0810, 0.2090
0.5000, 0.0000, 0.3180, 0.0820, 0.1360, 0.0692, 0.5500, 0.2000, 0.4078, 0.0850, 0.1360
0.6900, 0.0000, 0.3430, 0.1130, 0.2000, 0.1238, 0.5400, 0.4000, 0.4710, 0.1120, 0.2610
0.3400, 0.0000, 0.2630, 0.0870, 0.1970, 0.1200, 0.6300, 0.3000, 0.4249, 0.0960, 0.1130
0.7100, 1.0000, 0.2700, 0.0933, 0.2690, 0.1902, 0.4100, 0.6560, 0.5242, 0.0930, 0.1310
0.4700, 0.0000, 0.2720, 0.0800, 0.2080, 0.1456, 0.3800, 0.6000, 0.4804, 0.0920, 0.1740
0.4100, 0.0000, 0.3380, 0.1233, 0.1870, 0.1270, 0.4500, 0.4160, 0.4318, 0.1000, 0.2570
0.3400, 0.0000, 0.3300, 0.0730, 0.1780, 0.1146, 0.5100, 0.3490, 0.4127, 0.0920, 0.0550
0.5100, 0.0000, 0.2410, 0.0870, 0.2610, 0.1756, 0.6900, 0.4000, 0.4407, 0.0930, 0.0840
0.4300, 0.0000, 0.2130, 0.0790, 0.1410, 0.0788, 0.5300, 0.3000, 0.3829, 0.0900, 0.0420
0.5500, 0.0000, 0.2300, 0.0947, 0.1900, 0.1376, 0.3800, 0.5000, 0.4277, 0.1060, 0.1460
0.5900, 1.0000, 0.2790, 0.1010, 0.2180, 0.1442, 0.3800, 0.6000, 0.5187, 0.0950, 0.2120
0.2700, 1.0000, 0.3360, 0.1100, 0.2460, 0.1566, 0.5700, 0.4000, 0.5088, 0.0890, 0.2330
0.5100, 1.0000, 0.2270, 0.1030, 0.2170, 0.1624, 0.3000, 0.7000, 0.4812, 0.0800, 0.0910
0.4900, 1.0000, 0.2740, 0.0890, 0.1770, 0.1130, 0.3700, 0.5000, 0.4905, 0.0970, 0.1110
0.2700, 0.0000, 0.2260, 0.0710, 0.1160, 0.0434, 0.5600, 0.2000, 0.4419, 0.0790, 0.1520
0.5700, 1.0000, 0.2320, 0.1073, 0.2310, 0.1594, 0.4100, 0.5630, 0.5030, 0.1120, 0.1200
0.3900, 1.0000, 0.2690, 0.0930, 0.1360, 0.0754, 0.4800, 0.3000, 0.4143, 0.0990, 0.0670
0.6200, 1.0000, 0.3460, 0.1200, 0.2150, 0.1292, 0.4300, 0.5000, 0.5366, 0.1230, 0.3100
0.3700, 0.0000, 0.2330, 0.0880, 0.2230, 0.1420, 0.6500, 0.3400, 0.4357, 0.0820, 0.0940
0.4600, 0.0000, 0.2110, 0.0800, 0.2050, 0.1444, 0.4200, 0.5000, 0.4533, 0.0870, 0.1830
0.6800, 1.0000, 0.2350, 0.1010, 0.1620, 0.0854, 0.5900, 0.3000, 0.4477, 0.0910, 0.0660
0.5100, 0.0000, 0.3150, 0.0930, 0.2310, 0.1440, 0.4900, 0.4700, 0.5252, 0.1170, 0.1730
0.4100, 0.0000, 0.2080, 0.0860, 0.2230, 0.1282, 0.8300, 0.3000, 0.4078, 0.0890, 0.0720
0.5300, 0.0000, 0.2650, 0.0970, 0.1930, 0.1224, 0.5800, 0.3000, 0.4143, 0.0990, 0.0490
0.4500, 0.0000, 0.2420, 0.0830, 0.1770, 0.1184, 0.4500, 0.4000, 0.4220, 0.0820, 0.0640
0.3300, 0.0000, 0.1950, 0.0800, 0.1710, 0.0854, 0.7500, 0.2000, 0.3970, 0.0800, 0.0480
0.6000, 1.0000, 0.2820, 0.1120, 0.1850, 0.1138, 0.4200, 0.4000, 0.4984, 0.0930, 0.1780
0.4700, 1.0000, 0.2490, 0.0750, 0.2250, 0.1660, 0.4200, 0.5000, 0.4443, 0.1020, 0.1040
0.6000, 1.0000, 0.2490, 0.0997, 0.1620, 0.1066, 0.4300, 0.3770, 0.4127, 0.0950, 0.1320
0.3600, 0.0000, 0.3000, 0.0950, 0.2010, 0.1252, 0.4200, 0.4790, 0.5130, 0.0850, 0.2200
0.3600, 0.0000, 0.1960, 0.0710, 0.2500, 0.1332, 0.9700, 0.3000, 0.4595, 0.0920, 0.0570

Two closely related machine learning regression techniques are kernel ridge regression (KRR) and support vector regression (SVR). Both techniques use a kernel function (usually the radial basis function, RBF) to compare two data items for similarity. Both techniques must store training data in order to make predictions, but KRR stores all training items, while SVR eliminates some of the items, leaving just the “support vectors” that need to be stored.

KRR often gives slightly better prediction accuracy than SVR, is easier to train than SVR, can handle very large datasets (KRR can use the SGD training technique), and is much, much easier to implement from scratch than SVR (SVR must use the very ugly quadratic programming technique).

One morning before work, I got the idea of combining KRR and SVR. Briefly, I train a KRR model as normal using all training data. Then I identify training data items that are predicted “too well” and remove them, leaving just pseudo support vectors. The SVR idea is that items that are predicted too well don’t help model accuracy very much. Then I retrain a new KRR model using only the reduced training data. This gives a trimmed/sparse KRR model that approximates an SVR model.

A trimmed KRR model and a SVR model won’t be exactly equivalent because KRR minimizes mean squared error and SVR minimizes a weird loss function called epsilon-insensitive loss. And trimmed KRR removes some of the stored training items after training, while SVR removes training items during training. But the two techniques should give nearly the same model in terms of predictive accuracy.

In my mind, this technique gives the advantages of KRR (ability to handle very large datasets) and the advantages of SVR (fewer stored model items and weights than KRR. . . if the technique works. Bottom line: it worked well.

I put together a demo using the scikit KernelRidge module. And the sparse KRR idea worked quite nicely. The output of the demo is:

Begin sparse KRR approximation to SVR demo

Loading synthetic train (200) and test (40) data
Done

First three train X:
[-0.1660  0.4406 -0.9998 -0.3953 -0.7065]
[ 0.0776 -0.1616  0.3704 -0.5911  0.7562]
[-0.9452  0.3409 -0.1654  0.1174 -0.7192]

First three train y:
0.4840
0.1568
0.8054

Creating preliminary KRR RBF model
Setting gamma = 0.1000
Setting alpha = 0.0010
Done

Training KRR model
Done

Removing non-pseudo-support vectors
Using epsilon = 0.003000
Number of pseudo support vectors = 138

Re-training sparse KRR model
Done

Evaluating model

Accuracy (within 0.10) train = 0.9710
Accuracy (within 0.10) test = 0.9500

MSE train = 0.0001
MSE test = 0.0002

The demo data is synthetic demo. There are 200 training items and 40 test items.

After training on 200 data items, those items that were predicted with a small error of less than 0.004850 were removed. There were 93 such well-predicted items, leaving a reduced training dataset of 107 items. After training a new model on the reduced dataset, the sparse model scored 97.10% accuracy on the reduced training data (134 out of 138 correct) and 95.00% accuracy on the test data (38 out of 40 correct).

An optimized scikit SVR model created 90 support vectors (better than the sparse KRR 138 items), with 96.50% accuracy on the training data (not quite as good as the sparse KRR model), and 95.00% accuracy on the test data (identical to the sparse KRR model). In short, the sparse KRR model and the SVR model are very similar. The large number of hyperparameters involved with KRR and SVR makes exact comparison impossible in practice.

An interesting experiment.

I’m old enough to have seen all the James Bond films when they were first released — even the first five with actor Sean Connery as Bond. Every one of the first five films has at least one Asian actress, even if their presence was a bit sparse. Here is a memorable scene from “Dr. No” (1962), the very first Bond film. I saw it at the Fox Fullerton (California) theater on Harbor Blvd. It is my favorite Bond film.

On the left, the woman is saying, “I am Sister Rose, this is Sister Lily.” The scene takes place shortly after Bond and Honey Ryder (actress Ursula Andress) were captured and brought to Dr. No’s underground lair. Sister Rose was played by actress Michele Mok. Sister Lily was played by actress Yvonne Shima. One of the big questions among Bond fans is what happened to Rose and Lily. It is assumed/hoped that they both escaped, as many of Dr. No’s employees did, when Bond blew up Dr. No’s facility at the end of the movie.

The sparse KRR demo program. Replace the “lt” in the accuracy() function with the less-than Boolean symbol (my blog editor chokes on symbols).

# svr_via_krr_scikit.py
# train using KRR, remove some, retrain using KRR

import numpy as np
from sklearn.kernel_ridge import KernelRidge

# KernelRidge(alpha=1, *, kernel='linear', gamma=None,
# degree=3, coef0=1, kernel_params=None)

# -----------------------------------------------------------

np.set_printoptions(precision=4, suppress=True,
  floatmode='fixed', linewidth=60)

# -----------------------------------------------------------

def accuracy(model, data_X, data_y, pct_close):
  n = len(data_X)
  n_correct = 0; n_wrong = 0
  for i in range(n):
    x = data_X[i].reshape(1,-1)
    y = data_y[i]
    y_pred = model.predict(x)[0]

    if np.abs(y - y_pred) "lt" np.abs(y * pct_close):
      n_correct += 1
    else: 
      n_wrong += 1
  return n_correct / (n_correct + n_wrong)

def mse(model, data_X, data_y):
  n = len(data_X)
  sum = 0.0
  for i in range(n):
    actual_y = data_y[i]
    pred_y = model.predict(data_X[i].reshape(1, -1))[0]
    diff = actual_y - pred_y
    sum += diff * diff
  return sum /n

# -----------------------------------------------------------
# -----------------------------------------------------------

print("\nBegin sparse KRR approximation to SVR demo ")

np.set_printoptions(precision=4, suppress=True,
    floatmode='fixed')

print("\nLoading synthetic train (200) and test (40) data ")
train_Xy = np.loadtxt(".\\Data\\synthetic_train_200.txt",
  usecols=[0,1,2,3,4,5], delimiter=",")
train_X = train_Xy[:,[0,1,2,3,4]]
train_y = train_Xy[:,5]

test_Xy = np.loadtxt(".\\Data\\synthetic_test_40.txt",
  usecols=[0,1,2,3,4,5], delimiter=",")
test_X = test_Xy[:,[0,1,2,3,4]]
test_y = test_Xy[:,5]
print("Done ")

print("\nFirst three train X: ")
for i in range(3):
  print(train_X[i])
print("\nFirst three train y: ")
for i in range(3):
  print("%0.4f " % train_y[i])

print("\nCreating preliminry KRR RBF model ")
gamma = 0.1000
alpha = 0.0010
print("Setting gamma = %0.4f " % gamma)
print("Setting alpha = %0.4f " % alpha)
model = KernelRidge(kernel='rbf', gamma=gamma, alpha=alpha)
print("Done ")

print("\nTraining KRR model ")
model.fit(train_X, train_y)
print("Done ")

print("\nRemoving non-pseudo-support vectors ")
predictions = model.predict(train_X)
residuals = np.abs(train_y - predictions)
# smaller epsilon = more support vectors
# larger epsilon = fewer support vectors
epsilon = 0.003
print("Using epsilon = %0.6f " % epsilon)
# keep only points outside epsilon-tube (support vectors)
sv_indices = np.where(residuals > epsilon)[0]
X_sv = train_X[sv_indices]
y_sv = train_y[sv_indices]
print("Number of pseudo support vectors = " + \
  str(len(X_sv)))

# retrain
print("\nRe-training sparse KRR model ")
model = KernelRidge(kernel='rbf', gamma=gamma, alpha=alpha)
model.fit(X_sv, y_sv)
print("Done ")

print("\nEvaluating model ")
acc_train = accuracy(model, X_sv, y_sv, 0.10)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("\nAccuracy (within 0.10) train = %0.4f " % \
  acc_train)
print("Accuracy (within 0.10) test = %0.4f " % \
  acc_test)

mse_train = mse(model, X_sv, y_sv)
mse_test = mse(model, test_X, test_y)
print("\nMSE train = %0.4f " % mse_train)
print("MSE test = %0.4f " % mse_test)

Training data:

# synthetic_train_200.txt
#
-0.1660,  0.4406, -0.9998, -0.3953, -0.7065,  0.4840
 0.0776, -0.1616,  0.3704, -0.5911,  0.7562,  0.1568
-0.9452,  0.3409, -0.1654,  0.1174, -0.7192,  0.8054
 0.9365, -0.3732,  0.3846,  0.7528,  0.7892,  0.1345
-0.8299, -0.9219, -0.6603,  0.7563, -0.8033,  0.7955
 0.0663,  0.3838, -0.3690,  0.3730,  0.6693,  0.3206
-0.9634,  0.5003,  0.9777,  0.4963, -0.4391,  0.7377
-0.1042,  0.8172, -0.4128, -0.4244, -0.7399,  0.4801
-0.9613,  0.3577, -0.5767, -0.4689, -0.0169,  0.6861
-0.7065,  0.1786,  0.3995, -0.7953, -0.1719,  0.5569
 0.3888, -0.1716, -0.9001,  0.0718,  0.3276,  0.2500
 0.1731,  0.8068, -0.7251, -0.7214,  0.6148,  0.3297
-0.2046, -0.6693,  0.8550, -0.3045,  0.5016,  0.2129
 0.2473,  0.5019, -0.3022, -0.4601,  0.7918,  0.2613
-0.1438,  0.9297,  0.3269,  0.2434, -0.7705,  0.5171
 0.1568, -0.1837, -0.5259,  0.8068,  0.1474,  0.3307
-0.9943,  0.2343, -0.3467,  0.0541,  0.7719,  0.5581
 0.2467, -0.9684,  0.8589,  0.3818,  0.9946,  0.1092
-0.6553, -0.7257,  0.8652,  0.3936, -0.8680,  0.7018
 0.8460,  0.4230, -0.7515, -0.9602, -0.9476,  0.1996
-0.9434, -0.5076,  0.7201,  0.0777,  0.1056,  0.5664
 0.9392,  0.1221, -0.9627,  0.6013, -0.5341,  0.1533
 0.6142, -0.2243,  0.7271,  0.4942,  0.1125,  0.1661
 0.4260,  0.1194, -0.9749, -0.8561,  0.9346,  0.2230
 0.1362, -0.5934, -0.4953,  0.4877, -0.6091,  0.3810
 0.6937, -0.5203, -0.0125,  0.2399,  0.6580,  0.1460
-0.6864, -0.9628, -0.8600, -0.0273,  0.2127,  0.5387
 0.9772,  0.1595, -0.2397,  0.1019,  0.4907,  0.1611
 0.3385, -0.4702, -0.8673, -0.2598,  0.2594,  0.2270
-0.8669, -0.4794,  0.6095, -0.6131,  0.2789,  0.4700
 0.0493,  0.8496, -0.4734, -0.8681,  0.4701,  0.3516
 0.8639, -0.9721, -0.5313,  0.2336,  0.8980,  0.1412
 0.9004,  0.1133,  0.8312,  0.2831, -0.2200,  0.1782
 0.0991,  0.8524,  0.8375, -0.2102,  0.9265,  0.2150
-0.6521, -0.7473, -0.7298,  0.0113, -0.9570,  0.7422
 0.6190, -0.3105,  0.8802,  0.1640,  0.7577,  0.1056
 0.6895,  0.8108, -0.0802,  0.0927,  0.5972,  0.2214
 0.1982, -0.9689,  0.1870, -0.1326,  0.6147,  0.1310
-0.3695,  0.7858,  0.1557, -0.6320,  0.5759,  0.3773
-0.1596,  0.3581,  0.8372, -0.9992,  0.9535,  0.2071
-0.2468,  0.9476,  0.2094,  0.6577,  0.1494,  0.4132
 0.1737,  0.5000,  0.7166,  0.5102,  0.3961,  0.2611
 0.7290, -0.3546,  0.3416, -0.0983, -0.2358,  0.1332
-0.3652,  0.2438, -0.1395,  0.9476,  0.3556,  0.4170
-0.6029, -0.1466, -0.3133,  0.5953,  0.7600,  0.4334
-0.4596, -0.4953,  0.7098,  0.0554,  0.6043,  0.2775
 0.1450,  0.4663,  0.0380,  0.5418,  0.1377,  0.2931
-0.8636, -0.2442, -0.8407,  0.9656, -0.6368,  0.7429
 0.6237,  0.7499,  0.3768,  0.1390, -0.6781,  0.2185
-0.5499,  0.1850, -0.3755,  0.8326,  0.8193,  0.4399
-0.4858, -0.7782, -0.6141, -0.0008,  0.4572,  0.4197
 0.7033, -0.1683,  0.2334, -0.5327, -0.7961,  0.1776
 0.0317, -0.0457, -0.6947,  0.2436,  0.0880,  0.3345
 0.5031, -0.5559,  0.0387,  0.5706, -0.9553,  0.3107
-0.3513,  0.7458,  0.6894,  0.0769,  0.7332,  0.3170
 0.2205,  0.5992, -0.9309,  0.5405,  0.4635,  0.3532
-0.4806, -0.4859,  0.2646, -0.3094,  0.5932,  0.3202
 0.9809, -0.3995, -0.7140,  0.8026,  0.0831,  0.1600
 0.9495,  0.2732,  0.9878,  0.0921,  0.0529,  0.1289
-0.9476, -0.6792,  0.4913, -0.9392, -0.2669,  0.5966
 0.7247,  0.3854,  0.3819, -0.6227, -0.1162,  0.1550
-0.5922, -0.5045, -0.4757,  0.5003, -0.0860,  0.5863
-0.8861,  0.0170, -0.5761,  0.5972, -0.4053,  0.7301
 0.6877, -0.2380,  0.4997,  0.0223,  0.0819,  0.1404
 0.9189,  0.6079, -0.9354,  0.4188, -0.0700,  0.1907
-0.1428, -0.7820,  0.2676,  0.6059,  0.3936,  0.2790
 0.5324, -0.3151,  0.6917, -0.1425,  0.6480,  0.1071
-0.8432, -0.9633, -0.8666, -0.0828, -0.7733,  0.7784
-0.9444,  0.5097, -0.2103,  0.4939, -0.0952,  0.6787
-0.0520,  0.6063, -0.1952,  0.8094, -0.9259,  0.4836
 0.5477, -0.7487,  0.2370, -0.9793,  0.0773,  0.1241
 0.2450,  0.8116,  0.9799,  0.4222,  0.4636,  0.2355
 0.8186, -0.1983, -0.5003, -0.6531, -0.7611,  0.1511
-0.4714,  0.6382, -0.3788,  0.9648, -0.4667,  0.5950
 0.0673, -0.3711,  0.8215, -0.2669, -0.1328,  0.2677
-0.9381,  0.4338,  0.7820, -0.9454,  0.0441,  0.5518
-0.3480,  0.7190,  0.1170,  0.3805, -0.0943,  0.4724
-0.9813,  0.1535, -0.3771,  0.0345,  0.8328,  0.5438
-0.1471, -0.5052, -0.2574,  0.8637,  0.8737,  0.3042
-0.5454, -0.3712, -0.6505,  0.2142, -0.1728,  0.5783
 0.6327, -0.6297,  0.4038, -0.5193,  0.1484,  0.1153
-0.5424,  0.3282, -0.0055,  0.0380, -0.6506,  0.6613
 0.1414,  0.9935,  0.6337,  0.1887,  0.9520,  0.2540
-0.9351, -0.8128, -0.8693, -0.0965, -0.2491,  0.7353
 0.9507, -0.6640,  0.9456,  0.5349,  0.6485,  0.1059
-0.0462, -0.9737, -0.2940, -0.0159,  0.4602,  0.2606
-0.0627, -0.0852, -0.7247, -0.9782,  0.5166,  0.2977
 0.0478,  0.5098, -0.0723, -0.7504, -0.3750,  0.3335
 0.0090,  0.3477,  0.5403, -0.7393, -0.9542,  0.4415
-0.9748,  0.3449,  0.3736, -0.1015,  0.8296,  0.4358
 0.2887, -0.9895, -0.0311,  0.7186,  0.6608,  0.2057
 0.1570, -0.4518,  0.1211,  0.3435, -0.2951,  0.3244
 0.7117, -0.6099,  0.4946, -0.4208,  0.5476,  0.1096
-0.2929, -0.5726,  0.5346, -0.3827,  0.4665,  0.2465
 0.4889, -0.5572, -0.5718, -0.6021, -0.7150,  0.2163
-0.7782,  0.3491,  0.5996, -0.8389, -0.5366,  0.6516
-0.5847,  0.8347,  0.4226,  0.1078, -0.3910,  0.6134
 0.8469,  0.4121, -0.0439, -0.7476,  0.9521,  0.1571
-0.6803, -0.5948, -0.1376, -0.1916, -0.7065,  0.7156
 0.2878,  0.5086, -0.5785,  0.2019,  0.4979,  0.2980
 0.2764,  0.1943, -0.4090,  0.4632,  0.8906,  0.2960
-0.8877,  0.6705, -0.6155, -0.2098, -0.3998,  0.7107
-0.8398,  0.8093, -0.2597,  0.0614, -0.0118,  0.6502
-0.8476,  0.0158, -0.4769, -0.2859, -0.7839,  0.7715
 0.5751, -0.7868,  0.9714, -0.6457,  0.1448,  0.1175
 0.4802, -0.7001,  0.1022, -0.5668,  0.5184,  0.1090
 0.4458, -0.6469,  0.7239, -0.9604,  0.7205,  0.0779
 0.5175,  0.4339,  0.9747, -0.4438, -0.9924,  0.2879
 0.8678,  0.7158,  0.4577,  0.0334,  0.4139,  0.1678
 0.5406,  0.5012,  0.2264, -0.1963,  0.3946,  0.2088
-0.9938,  0.5498,  0.7928, -0.5214, -0.7585,  0.7687
 0.7661,  0.0863, -0.4266, -0.7233, -0.4197,  0.1466
 0.2277, -0.3517, -0.0853, -0.1118,  0.6563,  0.1767
 0.3499, -0.5570, -0.0655, -0.3705,  0.2537,  0.1632
 0.7547, -0.1046,  0.5689, -0.0861,  0.3125,  0.1257
 0.8186,  0.2110,  0.5335,  0.0094, -0.0039,  0.1391
 0.6858, -0.8644,  0.1465,  0.8855,  0.0357,  0.1845
-0.4967,  0.4015,  0.0805,  0.8977,  0.2487,  0.4663
 0.6760, -0.9841,  0.9787, -0.8446, -0.3557,  0.1509
-0.1203, -0.4885,  0.6054, -0.0443, -0.7313,  0.4854
 0.8557,  0.7919, -0.0169,  0.7134, -0.1628,  0.2002
 0.0115, -0.6209,  0.9300, -0.4116, -0.7931,  0.4052
-0.7114, -0.9718,  0.4319,  0.1290,  0.5892,  0.3661
 0.3915,  0.5557, -0.1870,  0.2955, -0.6404,  0.2954
-0.3564, -0.6548, -0.1827, -0.5172, -0.1862,  0.4622
 0.2392, -0.4959,  0.5857, -0.1341, -0.2850,  0.2470
-0.3394,  0.3947, -0.4627,  0.6166, -0.4094,  0.5325
 0.7107,  0.7768, -0.6312,  0.1707,  0.7964,  0.2757
-0.1078,  0.8437, -0.4420,  0.2177,  0.3649,  0.4028
-0.3139,  0.5595, -0.6505, -0.3161, -0.7108,  0.5546
 0.4335,  0.3986,  0.3770, -0.4932,  0.3847,  0.1810
-0.2562, -0.2894, -0.8847,  0.2633,  0.4146,  0.4036
 0.2272,  0.2966, -0.6601, -0.7011,  0.0284,  0.2778
-0.0743, -0.1421, -0.0054, -0.6770, -0.3151,  0.3597
-0.4762,  0.6891,  0.6007, -0.1467,  0.2140,  0.4266
-0.4061,  0.7193,  0.3432,  0.2669, -0.7505,  0.6147
-0.0588,  0.9731,  0.8966,  0.2902, -0.6966,  0.4955
-0.0627, -0.1439,  0.1985,  0.6999,  0.5022,  0.3077
 0.1587,  0.8494, -0.8705,  0.9827, -0.8940,  0.4263
-0.7850,  0.2473, -0.9040, -0.4308, -0.8779,  0.7199
 0.4070,  0.3369, -0.2428, -0.6236,  0.4940,  0.2215
-0.0242,  0.0513, -0.9430,  0.2885, -0.2987,  0.3947
-0.5416, -0.1322, -0.2351, -0.0604,  0.9590,  0.3683
 0.1055,  0.7783, -0.2901, -0.5090,  0.8220,  0.2984
-0.9129,  0.9015,  0.1128, -0.2473,  0.9901,  0.4776
-0.9378,  0.1424, -0.6391,  0.2619,  0.9618,  0.5368
 0.7498, -0.0963,  0.4169,  0.5549, -0.0103,  0.1614
-0.2612, -0.7156,  0.4538, -0.0460, -0.1022,  0.3717
 0.7720,  0.0552, -0.1818, -0.4622, -0.8560,  0.1685
-0.4177,  0.0070,  0.9319, -0.7812,  0.3461,  0.3052
-0.0001,  0.5542, -0.7128, -0.8336, -0.2016,  0.3803
 0.5356, -0.4194, -0.5662, -0.9666, -0.2027,  0.1776
-0.2378,  0.3187, -0.8582, -0.6948, -0.9668,  0.5474
-0.1947, -0.3579,  0.1158,  0.9869,  0.6690,  0.2992
 0.3992,  0.8365, -0.9205, -0.8593, -0.0520,  0.3154
-0.0209,  0.0793,  0.7905, -0.1067,  0.7541,  0.1864
-0.4928, -0.4524, -0.3433,  0.0951, -0.5597,  0.6261
-0.8118,  0.7404, -0.5263, -0.2280,  0.1431,  0.6349
 0.0516, -0.8480,  0.7483,  0.9023,  0.6250,  0.1959
-0.3212,  0.1093,  0.9488, -0.3766,  0.3376,  0.2735
-0.3481,  0.5490, -0.3484,  0.7797,  0.5034,  0.4379
-0.5785, -0.9170, -0.3563, -0.9258,  0.3877,  0.4121
 0.3407, -0.1391,  0.5356,  0.0720, -0.9203,  0.3458
-0.3287, -0.8954,  0.2102,  0.0241,  0.2349,  0.3247
-0.1353,  0.6954, -0.0919, -0.9692,  0.7461,  0.3338
 0.9036, -0.8982, -0.5299, -0.8733, -0.1567,  0.1187
 0.7277, -0.8368, -0.0538, -0.7489,  0.5458,  0.0830
 0.9049,  0.8878,  0.2279,  0.9470, -0.3103,  0.2194
 0.7957, -0.1308, -0.5284,  0.8817,  0.3684,  0.2172
 0.4647, -0.4931,  0.2010,  0.6292, -0.8918,  0.3371
-0.7390,  0.6849,  0.2367,  0.0626, -0.5034,  0.7039
-0.1567, -0.8711,  0.7940, -0.5932,  0.6525,  0.1710
 0.7635, -0.0265,  0.1969,  0.0545,  0.2496,  0.1445
 0.7675,  0.1354, -0.7698, -0.5460,  0.1920,  0.1728
-0.5211, -0.7372, -0.6763,  0.6897,  0.2044,  0.5217
 0.1913,  0.1980,  0.2314, -0.8816,  0.5006,  0.1998
 0.8964,  0.0694, -0.6149,  0.5059, -0.9854,  0.1825
 0.1767,  0.7104,  0.2093,  0.6452,  0.7590,  0.2832
-0.3580, -0.7541,  0.4426, -0.1193, -0.7465,  0.5657
-0.5996,  0.5766, -0.9758, -0.3933, -0.9572,  0.6800
 0.9950,  0.1641, -0.4132,  0.8579,  0.0142,  0.2003
-0.4717, -0.3894, -0.2567, -0.5111,  0.1691,  0.4266
 0.3917, -0.8561,  0.9422,  0.5061,  0.6123,  0.1212
-0.0366, -0.1087,  0.3449, -0.1025,  0.4086,  0.2475
 0.3633,  0.3943,  0.2372, -0.6980,  0.5216,  0.1925
-0.5325, -0.6466, -0.2178, -0.3589,  0.6310,  0.3568
 0.2271,  0.5200, -0.1447, -0.8011, -0.7699,  0.3128
 0.6415,  0.1993,  0.3777, -0.0178, -0.8237,  0.2181
-0.5298, -0.0768, -0.6028, -0.9490,  0.4588,  0.4356
 0.6870, -0.1431,  0.7294,  0.3141,  0.1621,  0.1632
-0.5985,  0.0591,  0.7889, -0.3900,  0.7419,  0.2945
 0.3661,  0.7984, -0.8486,  0.7572, -0.6183,  0.3449
 0.6995,  0.3342, -0.3113, -0.6972,  0.2707,  0.1712
 0.2565,  0.9126,  0.1798, -0.6043, -0.1413,  0.2893
-0.3265,  0.9839, -0.2395,  0.9854,  0.0376,  0.4770
 0.2690, -0.1722,  0.9818,  0.8599, -0.7015,  0.3954
-0.2102, -0.0768,  0.1219,  0.5607, -0.0256,  0.3949
 0.8216, -0.9555,  0.6422, -0.6231,  0.3715,  0.0801
-0.2896,  0.9484, -0.7545, -0.6249,  0.7789,  0.4370
-0.9985, -0.5448, -0.7092, -0.5931,  0.7926,  0.5402

Test data:

# synthetic_test_40.txt
#
 0.7462,  0.4006, -0.0590,  0.6543, -0.0083,  0.1935
 0.8495, -0.2260, -0.0142, -0.4911,  0.7699,  0.1078
-0.2335, -0.4049,  0.4352, -0.6183, -0.7636,  0.5088
 0.1810, -0.5142,  0.2465,  0.2767, -0.3449,  0.3136
-0.8650,  0.7611, -0.0801,  0.5277, -0.4922,  0.7140
-0.2358, -0.7466, -0.5115, -0.8413, -0.3943,  0.4533
 0.4834,  0.2300,  0.3448, -0.9832,  0.3568,  0.1360
-0.6502, -0.6300,  0.6885,  0.9652,  0.8275,  0.3046
-0.3053,  0.5604,  0.0929,  0.6329, -0.0325,  0.4756
-0.7995,  0.0740, -0.2680,  0.2086,  0.9176,  0.4565
-0.2144, -0.2141,  0.5813,  0.2902, -0.2122,  0.4119
-0.7278, -0.0987, -0.3312, -0.5641,  0.8515,  0.4438
 0.3793,  0.1976,  0.4933,  0.0839,  0.4011,  0.1905
-0.8568,  0.9573, -0.5272,  0.3212, -0.8207,  0.7415
-0.5785,  0.0056, -0.7901, -0.2223,  0.0760,  0.5551
 0.0735, -0.2188,  0.3925,  0.3570,  0.3746,  0.2191
 0.1230, -0.2838,  0.2262,  0.8715,  0.1938,  0.2878
 0.4792, -0.9248,  0.5295,  0.0366, -0.9894,  0.3149
-0.4456,  0.0697,  0.5359, -0.8938,  0.0981,  0.3879
 0.8629, -0.8505, -0.4464,  0.8385,  0.5300,  0.1769
 0.1995,  0.6659,  0.7921,  0.9454,  0.9970,  0.2330
-0.0249, -0.3066, -0.2927, -0.4923,  0.8220,  0.2437
 0.4513, -0.9481, -0.0770, -0.4374, -0.9421,  0.2879
-0.3405,  0.5931, -0.3507, -0.3842,  0.8562,  0.3987
 0.9538,  0.0471,  0.9039,  0.7760,  0.0361,  0.1706
-0.0887,  0.2104,  0.9808,  0.5478, -0.3314,  0.4128
-0.8220, -0.6302,  0.0537, -0.1658,  0.6013,  0.4306
-0.4123, -0.2880,  0.9074, -0.0461, -0.4435,  0.5144
 0.0060,  0.2867, -0.7775,  0.5161,  0.7039,  0.3599
-0.7968, -0.5484,  0.9426, -0.4308,  0.8148,  0.2979
 0.7811,  0.8450, -0.6877,  0.7594,  0.2640,  0.2362
-0.6802, -0.1113, -0.8325, -0.6694, -0.6056,  0.6544
 0.3821,  0.1476,  0.7466, -0.5107,  0.2592,  0.1648
 0.7265,  0.9683, -0.9803, -0.4943, -0.5523,  0.2454
-0.9049, -0.9797, -0.0196, -0.9090, -0.4433,  0.6447
-0.4607,  0.1811, -0.2389,  0.4050, -0.0078,  0.5229
 0.2664, -0.2932, -0.4259, -0.7336,  0.8742,  0.1834
-0.4507,  0.1029, -0.6294, -0.1158, -0.6294,  0.6081
 0.8948, -0.0124,  0.9278,  0.2899, -0.0314,  0.1534
-0.1323, -0.8813, -0.0146, -0.0697,  0.6135,  0.2386