I recently implemented support vector regression (SVR) from scratch using the C# language, trained using stochastic sub-gradient descent (SSGD). The SVR system seemed to work well but I figured I’d compare it with the gold standard scikit-learn SVR module. Bottom line: the results of the two systems are essentially the same, but the scikit SVR system gives better sparsity (fewer support vectors).
For my demos, I used a set of synthetic data with 5 predictors. There are 200 training items and 40 test items.
Scratch C# results:
Number support vectors = 119 Train acc (within 0.05) = 0.8500 Test acc (within 0.05) = 0.8000 Train MSE = 0.0001 Test MSE = 0.0001
Scikit SVR results:
Number support vectors = 92 Accuracy (within 0.05) train = 0.8350 Accuracy (within 0.05) test = 0.8000 MSE train = 0.0001 MSE test = 0.0001
Because of the large number of hyperparameters involved, the comparison results are not conclusive. To the best of my knowledge, I am the only person who has implemented and published an SVR with SSGD training system.
Support vector regression is closely related to kernel ridge regression. Both techniques use the kernel trick to handle complex data. Both techniques have one model weight per data item (support vector items or training items). In the late 1990s, support vector regression experienced a brief period of popularity in the data science community, mostly due (in my opinion) to the novelty of the SMO training algorithm.
However, it quickly became clear that 1.) kernel ridge regression is simpler to implement than SVR, 2.) KRR can use simple closed-form training while SVR cannot, 3.) KRR parameters are usually easier to tune than SVR parameters, and 4.) KRR almost always gives prediction accuracy at least as good as, and often better than, SVR. So, support vector regression quickly faded from popularity in favor of kernel ridge regression. That said, SVR is still used often in certain problem domains such as biology and chemistry.
Comparing C# vs. Python is one thing. Comparing high school graduation ceremonies is another thing. At graduation season in June, I always feel cheated because I live in an area dominated by employees from Microsoft, Amazon, and Google. My city is an area where 98% of the population is White or Asian. I have literally never seen a problem minority person in my local supermarket, or walking in my neighborhood — ever.
The local high school graduation ceremonies in my area are boring — families show up, are dressed nicely, and celebrate education. Other areas of the country have high school graduation ceremonies that are far more entertaining, and are guaranteed to feature multiple brawls.
Left: Ripley HS (Lauderdale County, Tennessee) 2026 graduation chaos. Right: John Marshall HS (Richmond, Virginia) 2026 graduation melee.
Demo C# program. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols (my blog editor chokes on symbols).
using System;
using System.IO;
using System.Collections.Generic;
// kernel SVR with SSGD training
// hard-wired RBF kernel function
namespace SupportVectorRegressionSGD
{
internal class SupportVectorRegressionSGDProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin C# kernel support " +
"vector regression with SSGD ");
Console.WriteLine("\nLoading train (200) and" +
" test (40) data ");
string trainFile =
"..\\..\\..\\Data\\synthetic_train_200.txt";
double[][] trainX =
Utils.MatLoad(trainFile,
new int[] { 0, 1, 2, 3, 4 }, ',', "#");
double[] trainY =
Utils.MatToVec(Utils.MatLoad(trainFile,
new int[] { 5 }, ',', "#"));
string testFile =
"..\\..\\..\\Data\\synthetic_test_40.txt";
double[][] testX =
Utils.MatLoad(testFile,
new int[] { 0, 1, 2, 3, 4 }, ',', "#");
double[] testY =
Utils.MatToVec(Utils.MatLoad(testFile,
new int[] { 5 }, ',', "#"));
Console.WriteLine("Done ");
Console.WriteLine("\nFirst three X predictors: ");
for (int i = 0; i "lt" 3; ++i)
Utils.VecShow(trainX[i], 4, 9);
Console.WriteLine("\nFirst three target y: ");
for (int i = 0; i "lt" 3; ++i)
Console.WriteLine(trainY[i].ToString("F4").
PadLeft(8));
Console.WriteLine("\nCreating SVR object");
double gamma = 0.30; // RBF param
double epsilon = 0.010;
double C = 1.0;
double lrnRate = 0.001;
int maxEpochs = 10000;
double tol = 1.0e-4;
Console.WriteLine("Setting RBF gamma = " +
gamma.ToString("F4"));
Console.WriteLine("Setting epsilon = " +
epsilon.ToString("F6"));
Console.WriteLine("Setting C = " +
C.ToString("F2"));
Console.WriteLine("Setting lrnRate = " +
lrnRate.ToString("F4"));
Console.WriteLine("Setting maxEpochs = " +
maxEpochs);
Console.WriteLine("Setting tol = " +
tol.ToString("F6"));
SVR model = new SVR(gamma, epsilon, C,
lrnRate, maxEpochs, tol, seed: 0);
Console.WriteLine("Done ");
Console.WriteLine("\nTraining SVR model using" +
" SGD ");
model.Train(trainX, trainY);
Console.WriteLine("Done ");
//Console.WriteLine("\nModel alpha (weights): ");
//Utils.VecShow(model.alpha, 4, 9);
Console.WriteLine("\nModel bias = " +
model.b.ToString("F4"));
Console.WriteLine("\nNumber supp vectors = " +
model.suppX.Length);
Console.WriteLine("\nEvaluating model ");
double trainAcc =
model.Accuracy(trainX, trainY, 0.05);
double testAcc =
model.Accuracy(testX, testY, 0.05);
Console.WriteLine("\nTrain acc (within 0.05) = " +
trainAcc.ToString("F4"));
Console.WriteLine("Test acc (within 0.05) = " +
testAcc.ToString("F4"));
double trainMSE = model.MSE(trainX, trainY);
double testMSE = model.MSE(testX, testY);
Console.WriteLine("\nTrain MSE = " +
trainMSE.ToString("F4"));
Console.WriteLine("Test MSE = " +
testMSE.ToString("F4"));
Console.WriteLine("\nEnd SVR with SSGD training demo ");
Console.ReadLine();
} // Main()
} // class Program
// ========================================================
public class SVR
{
public double gamma; // for RBF kernel
public double epsilon;
public double C; // weight regularization
public double[][] suppX; // needed for pred
public double[] suppY;
public double[] alpha; // one per trainX item
public double b; // bias
public double lrnRate; // for SGD training
public int maxEpochs;
public double tol;
public Random rnd;
// ------------------------------------------------------
public SVR(double gamma, double epsilon, double C,
double lrnRate, int maxEpochs, double tol,
int seed = 0)
{
this.gamma = gamma;
this.epsilon = epsilon;
this.C = C;
this.suppX = new double[0][]; // compiler happy
this.suppY = new double[0];
this.lrnRate = lrnRate;
this.maxEpochs = maxEpochs;
this.tol = tol;
this.alpha = new double[0];
this.b = 0.0;
this.rnd = new Random(seed); // shuffle train order
} // ctor
// ------------------------------------------------------
public void Train(double[][] trainX, double[] trainY)
{
this.suppX = trainX;
this.suppY = trainY;
int n = trainX.Length;
// init weights
this.alpha = new double[n];
double lo = -0.01; double hi = 0.01; // not needed
for (int i = 0; i "lt" n; ++i)
this.alpha[i] =
(hi - lo) * this.rnd.NextDouble() + lo;
this.b = 0.0;
// precompute all rbf values to K for fast train
// not feasible for huge datasets
double[][] K = this.MakeK(trainX);
// set up indices for random order SGD training
int[] indices = Utils.VecRange(n); // 0, 1, 2, ..
double lamda = 1.0 / this.C;
int progressFreq = (int)(this.maxEpochs / 5);
// main sub-gradient processing loop
for (int epoch = 0; epoch "lt" this.maxEpochs; ++epoch)
{
this.Shuffle(indices);
for (int i = 0; i "lt" indices.Length; ++i)
{
int idx = indices[i];
double predY = 0.0;
for (int j = 0; j "lt" this.alpha.Length; ++j)
predY += this.alpha[j] * K[idx][j]; // fast
predY += this.b;
double error = predY - trainY[idx];
double gradLoss;
bool insideTube = false;
if (error "gt" this.epsilon)
gradLoss = 1.0;
else if (error "lt" -this.epsilon)
gradLoss = -1.0;
else
{
gradLoss = 0.0;
insideTube = true;
}
// local kernel regularization gradient
double gradReg = this.alpha[idx] * K[idx][idx];
// decoupled updates to the active index
this.alpha[idx] -= this.lrnRate *
(lamda * gradReg + gradLoss);
this.b -= this.lrnRate * gradLoss;
// force tiny weights to 0
if (insideTube == true &&
Math.Abs(this.alpha[idx]) "lt" this.tol)
this.alpha[idx] = 0.0;
// in-loop clip to bound updates mid-flight
if (this.alpha[idx] "lt" -this.C)
this.alpha[idx] = -this.C;
else if (this.alpha[idx] "gt" this.C)
this.alpha[idx] = this.C;
} // each item
// show training progress every few epochs
if (epoch % progressFreq == 0)
{
double mse =
this.MSE(trainX, trainY);
double acc =
this.Accuracy(trainX, trainY, 0.05);
string s1 = "epoch = " +
epoch.ToString().PadLeft(6);
string s2 = " MSE = " +
mse.ToString("F4");
string s3 = " acc = " + acc.ToString("F4");
Console.WriteLine(s1 + s2 + s3);
}
} // each epoch
// final global clip
for (int i = 0; i "lt" n; ++i)
{
if (this.alpha[i] "lt" -this.C)
this.alpha[i] = -this.C;
else if (this.alpha[i] "gt" this.C)
this.alpha[i] = this.C;
}
// prune: store only explicit support vectors
List"lt"int"gt" svLst = new List"lt"int"gt"();
for (int i = 0; i "lt" this.alpha.Length; ++i)
{
if (Math.Abs(this.alpha[i]) "gt" 1.0e-5)
svLst.Add(i);
}
int[] svMask = svLst.ToArray();
this.suppX = Utils.MatSelectRows(trainX, svMask);
this.suppY = Utils.VecSelectItems(trainY, svMask);
this.alpha = Utils.VecSelectItems(this.alpha, svMask);
return; // all done
} // Train
// ------------------------------------------------------
private void Shuffle(int[] indices)
{
// Fisher-Yates helper for Train()
for (int i = 0; i "lt" indices.Length; ++i)
{
int ri = this.rnd.Next(i, indices.Length);
int tmp = indices[i];
indices[i] = indices[ri];
indices[ri] = tmp;
}
} // Shuffle
// ------------------------------------------------------
private double RBF(double[] v1, double[] v2)
{
int n = v1.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
{
double d = v1[i] - v2[i];
sum += d * d;
}
double result = Math.Exp(-1 * this.gamma * sum);
return result;
}
// ------------------------------------------------------
private double[][] MakeK(double[][] X)
{
// Kernel-Gram matrix helper for Train()
// pre-compute all similarities, to avoid re-computes
int n = X.Length;
double[][] result = Utils.MatMake(n, n);
for (int i = 0; i "lt" n; ++i)
for (int j = 0; j "lt" n; ++j)
result[i][j] = this.RBF(X[i], X[j]);
return result;
}
// ------------------------------------------------------
public double Predict(double[] x)
{
int n = this.suppX.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
{
double[] xx = this.suppX[i];
double k = this.RBF(x, xx);
sum += this.alpha[i] * k;
}
return sum + this.b;
}
// ------------------------------------------------------
public double Accuracy(double[][] dataX,
double[] dataY, double pctClose)
{
int numCorrect = 0; int numWrong = 0;
int n = dataX.Length;
for (int i = 0; i "lt" n; ++i)
{
double[] x = dataX[i];
double actualY = dataY[i];
double predY = this.Predict(x);
if (Math.Abs(actualY - predY) "lt"
Math.Abs(actualY * pctClose))
++numCorrect;
else
++numWrong;
}
return (numCorrect * 1.0) / n;
}
// ------------------------------------------------------
public double MSE(double[][] dataX, double[] dataY)
{
double sum = 0.0;
int n = dataX.Length;
for (int i = 0; i "lt" n; ++i)
{
double[] x = dataX[i];
double actualY = dataY[i];
double predY = this.Predict(x);
sum += (actualY - predY) * (actualY - predY);
}
return sum / n;
}
// ------------------------------------------------------
} // class KRR
// ========================================================
public class Utils
{
// ------------------------------------------------------
public static double[][] MatLoad(string fn,
int[] usecols, char sep, string comment)
{
List"lt"double[]"gt" result =
new List"lt"double[]"gt"();
string line = "";
FileStream ifs = new FileStream(fn, FileMode.Open);
StreamReader sr = new StreamReader(ifs);
while ((line = sr.ReadLine()) != null)
{
if (line.StartsWith(comment) == true)
continue;
string[] tokens = line.Split(sep);
List"lt"double"gt" lst = new List"lt"double"gt"();
for (int j = 0; j "lt" usecols.Length; ++j)
lst.Add(double.Parse(tokens[usecols[j]]));
double[] row = lst.ToArray();
result.Add(row);
}
sr.Close(); ifs.Close();
return result.ToArray();
}
// ------------------------------------------------------
public static double[] MatToVec(double[][] X)
{
int nRows = X.Length;
int nCols = X[0].Length;
double[] result = new double[nRows * nCols];
int k = 0;
for (int i = 0; i "lt" nRows; ++i)
for (int j = 0; j "lt" nCols; ++j)
result[k++] = X[i][j];
return result;
}
// ------------------------------------------------------
public static double[][] MatSelectRows(double[][] X,
int[] rows)
{
int nRowsSrc = X.Length;
int nColsSrc = X[0].Length;
int n = rows.Length;
double[][] result = MatMake(n, nColsSrc);
for (int i = 0; i "lt" n; ++i) // i pts into result
{
int srcRow = rows[i];
for (int j = 0; j "lt" nColsSrc; ++j)
{
result[i][j] = X[srcRow][j];
}
}
return result;
}
// ------------------------------------------------------
public static double[][] MatMake(int nRows, int nCols)
{
double[][] result = new double[nRows][];
for (int i = 0; i "lt" nRows; ++i)
result[i] = new double[nCols];
return result;
}
// ------------------------------------------------------
public static double VecMean(double[] vec)
{
int n = vec.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
sum += vec[i];
double result = sum / n;
return result;
}
// ------------------------------------------------------
public static int[] VecRange(int n)
{
int[] result = new int[n];
for (int i = 0; i "lt" n; ++i)
result[i] = i;
return result;
}
// ------------------------------------------------------
public static double[] VecSelectItems(double[] vec,
int[] idxs)
{
int n = idxs.Length;
double[] result = new double[n];
for (int i = 0; i "lt" n; ++i)
{
result[i] = vec[idxs[i]];
}
return result;
}
// ------------------------------------------------------
public static void VecShow(int[] vec, int wid)
{
for (int i = 0; i "lt" vec.Length; ++i)
Console.Write(vec[i].ToString().PadLeft(wid));
Console.WriteLine("");
}
// ------------------------------------------------------
public static void MatShow(double[][] M, int dec, int wid)
{
int nRows = M.Length; int nCols = M[0].Length;
double small = 1.0 / Math.Pow(10, dec);
for (int i = 0; i "lt" nRows; ++i)
{
for (int j = 0; j "lt" nCols; ++j)
{
double v = M[i][j];
if (Math.Abs(v) "lt" small) v = 0.0;
Console.Write(v.ToString("F" + dec).
PadLeft(wid));
}
Console.WriteLine("");
}
}
// ------------------------------------------------------
public static void VecShow(double[] vec, int dec, int wid)
{
for (int i = 0; i "lt" vec.Length; ++i)
Console.Write(vec[i].ToString("F" + dec).PadLeft(wid));
Console.WriteLine("");
}
// ------------------------------------------------------
} // class Utils
// ========================================================
} // ns
Demo scikit Python program. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols.
# svr_scikit.py
# support vector regression for a synthetic 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 demo ")
print("\nLoading synthetic train (200) and test (40) data ")
train_file = ".\\Data\\synthetic_train_200.txt"
cols_X = [0,1,2,3,4]
col_y = 5
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\\synthetic_test_40.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 ")
print("\nFirst three X predictors: ")
print(train_X[0:3,:])
print("\nFirst three y targets: ")
for i in range(3):
print("%9.4f" % train_y[i])
print("\nCreating scikit SVR model ")
gamma = 0.30 # more reasonable
C = 1.0000
epsilon = 0.010
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("\nNumber support vectors = ")
print(len(model.support_))
print("\nModel bias = %0.4f " % model.intercept_[0])
print("\nEvaluating model ")
acc_train = accuracy(model, train_X, train_y, 0.05)
acc_test = accuracy(model, test_X, test_y, 0.05)
print("\nAccuracy (within 0.05) train = %0.4f " % \
acc_train)
print("Accuracy (within 0.05) 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:
# 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
.NET Test Automation Recipes
Software Testing
SciPy Programming Succinctly
Keras Succinctly
R Programming
Visual Studio Live
Microsoft MLADS Conference
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Machine Learning Week
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