An Extra Trees Regressor (“Extremely Randomized Trees”) is an ensemble machine learning algorithm that builds multiple randomized decision trees to predict continuous numerical values. It differs from Random Forest regressions by introducing greater randomization during node splitting and utilizing the entire original dataset to train each tree rather than using samples of the original dataset.
One weekend I figured I’d implement Extra Trees Regression, from scratch, using Python and NumPy. The process took me a few hours, but was manageable because I have quite a bit of experience with tree-based systems.
The output of my demo:
Extra trees regression scratch Python NumPy Loading synthetic train (200), test (40) data Done First three X predictors: [-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 y targets: 0.4840 0.1568 0.8054 Setting n_estimators = 200 Setting max_depth = 6 Setting max_features = 4 Accuracy on train (within 0.10) = 0.7700 Accuracy on test (within 0.10) = 0.7250 MSE on train = 0.0006 MSE on test = 0.0012 Predicting for: [[-0.1660 0.4406 -0.9998 -0.3953 -0.7065]] Predicted y = 0.4930 SCIKIT: Accuracy on train (within 0.10) = 0.7750 Accuracy on test (within 0.10) = 0.6750 MSE on train = 0.0006 MSE on test = 0.0012 Done
The data is synthetic. It was generated by a neural network with random weights and biases. There are five predictor values and one value to predict. There are 200 training items and 40 test items.
Extra Trees Regression is an ensemble technique. For my demo, I used a collection of 200 base decision trees. The final prediction is the average of the 200 base trees. The base trees are exactly like standard decision trees, except, during construction, at each node, a base Extra Tree picks one value at random from each active column, and then uses the one value that gives the best split — a separation of rows of data that has the lowest variance (so that the left child nodes and right child nodes have relatively similar target y values).
The ideas are suprisingly subtle and implementation is extremely tricky.
The output of my from-scratch demo is very close to the output from the scikit-learn ExtraTreesRegressor module. The output wasn’t expected to be identical because Extra Trees Regression is fundamentally random.
Extra Trees Regression has no super powers — it’s just math and computer science. When I was a young man, I loved, and learned to read from, comic books of the early 1960s. I especially loved heros who had no special powers — they relied on just their intelligence — Batman, Green Arrow, Adam Strange, and Iron Man.
Left: The first apearance of Iron Man was in the anthology series “Tales of Suspense” #40 (March 1963). Iron Man had a plain steel colored suit.
Center: In the next issue, #41 (April 1963), Iron Man’s suit changed to a gold color.
Right: In issue #48 (December 1963), the suit changed to red and gold. Iron Man got his own title in May 1968.
Demo program. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols. (My blog editor chokes on symbols).
# extra_trees_regression_scratch.py
import numpy as np
np.set_printoptions(precision=4, suppress=True,
floatmode='fixed', linewidth=120)
# ===========================================================
class MyExtraTreesRegressor:
def __init__(self, n_estimators=100, max_depth=3,
min_samples_split=2, max_features='auto',
RandomState=0):
self.n_estimators = n_estimators
self.max_depth = max_depth
self.min_samples_split = min_samples_split
self.max_features = max_features
self.RandomState = RandomState
self.trees = []
self.rng = np.random.RandomState(RandomState)
def fit(self, train_X, train_y):
X = np.asarray(train_X)
n_samples, n_features = X.shape
# map scikit-learn standard max_features to your
# n_split_cols parameter
if self.max_features == 'auto' or self.max_features is None:
n_split_cols = n_features
elif self.max_features == 'sqrt':
n_split_cols = int(np.sqrt(n_features))
elif self.max_features == 'log2':
n_split_cols = int(np.log2(n_features))
else:
n_split_cols = int(self.max_features)
n_split_cols = max(1, min(n_split_cols, n_features))
self.trees = []
for _ in range(self.n_estimators):
tree_seed = self.rng.randint(0, 1000000)
# instantiate our specialized base tree
tree = MyExtraTreesBaseTree(
max_depth=self.max_depth,
min_samples=self.min_samples_split,
min_leaf=1,
n_split_cols=n_split_cols,
save_rows=False,
seed=tree_seed
)
tree.fit(train_X, train_y)
self.trees.append(tree)
return self
def predict(self, X):
X = np.asarray(X)
preds = np.array([tree.predict(X) for tree in self.trees])
return np.mean(preds, axis=0)
# ===========================================================
# -----------------------------------------------------------
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
# print("Correct = " + str(n_correct))
# print("Wrong = " + str(n_wrong))
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):
x = data_X[i].reshape(1,-1)
y = data_y[i]
y_pred = model.predict(x)[0]
# print(y_pred); input()
sum += (y - y_pred) * (y - y_pred)
return sum / n
# -----------------------------------------------------------
# ===========================================================
class MyExtraTreesBaseTree:
# identical to MyDecisionTreeRegressor except best_split()
def __init__(self, max_depth=3, min_samples=2,
min_leaf=1, n_split_cols=-1, save_rows=False,
seed=0):
self.max_depth = max_depth
self.min_samples = min_samples # to split
self.min_leaf = min_leaf # after split
self.n_split_cols = n_split_cols # -1 all cols
self.save_rows = save_rows
self.rnd = np.random.RandomState(seed)
self.tree = [] # list: no recursive, no ptrs
num_nodes = 2**(max_depth + 1) - 1
for i in range(num_nodes):
self.tree.append(None)
self.train_X = None
self.train_y = None
# ...............................................
class Node:
def __init__(self):
self.id = -1
self.col_idx = -1 # aka split col
self.thresh = 0.0 # aka split val
self.left = -1
self.right = -1
self.value = 0.0 # predicted y
self.is_leaf = False
self.rows = [] # associated rows in train
# ...............................................
def fit(self, train_X, train_y):
# aka train(), build_tree()
# self.train_X = np.array(train_X) # safety
# self.train_y = np.array(train_y)
self.train_X = train_X
self.train_y = train_y
max_id = 2**(self.max_depth+1) - 2 # md = 3, m_id = 14
max_start_id = 2**self.max_depth - 1 # md = 3, ms = 7
# prep root node
all_rows = []
for i in range(len(self.train_X)): # or use arange
all_rows.append(i)
grand_mean = self.tree_target_mean(all_rows)
root = self.Node()
root.id = 0
root.value = grand_mean
root.is_leaf = False
root.rows = all_rows
self.tree[0] = root
for i in range(len(self.tree)): # each node
curr_node = self.tree[i] # convenience
if curr_node is None: continue
# if node too deep to have children
# or not enough rows to split, leave children alone
if curr_node.id "gte" max_start_id or \
len(curr_node.rows) "lt" self.min_samples:
curr_node.is_leaf = True
continue
# try to split curr node
col_idx, split_val = self.best_split(curr_node.rows)
if col_idx == -1: # bad split
curr_node.is_leaf = True
curr_node.left = -1
curr_node.right = -1
continue
# got good split info
curr_node.col_idx = col_idx
curr_node.thresh = split_val
# make rows for the children
left_idxs = []
right_idxs = []
for k in range(len(curr_node.rows)):
r = curr_node.rows[k]
if self.train_X[r][col_idx] "lte" split_val:
left_idxs.append(r)
else:
right_idxs.append(r)
# make left child
left_id = curr_node.id * 2 + 1
if left_id "lte" max_id and len(left_idxs) "gte" \
self.min_leaf:
curr_node.left = left_id
left_node = self.Node()
left_node.id = left_id
left_node.rows = left_idxs
left_node.value = \
self.tree_target_mean(left_node.rows)
self.tree[left_id] = left_node
else:
curr_node.left = -1
# make right child
right_id = curr_node.id * 2 + 2
if right_id "lte" max_id and len(right_idxs) "gte" \
self.min_leaf:
curr_node.right = right_id
right_node = self.Node()
right_node.id = right_id
right_node.rows = right_idxs
right_node.value = \
self.tree_target_mean(right_node.rows)
self.tree[right_id] = right_node
else:
curr_node.right = -1
if curr_node.left == -1 and curr_node.right == -1:
curr_node.is_leaf = True
# zap away rows to save space if in ensemble
if self.save_rows == False:
for k in range(len(self.tree)):
if self.tree[k] is not None:
self.tree[k].rows = None
# ---------------------------------------------------------
def predict_one(self, x):
# x is a vector
curr_idx = 0
last_valid_value = 0.0
while curr_idx != -1 and curr_idx "lt" len(self.tree):
curr_node = self.tree[curr_idx]
if curr_node is None: break # safety check
last_valid_value = curr_node.value
if curr_node.is_leaf == True: break
if x[curr_node.col_idx] "lte" curr_node.thresh:
curr_idx = curr_node.left
else:
curr_idx = curr_node.right
return last_valid_value
# ---------------------------------------------------------
def predict(self, X):
# X is a matrix
n = len(X)
result = np.zeros(n)
for i in range(n):
result[i] = self.predict_one(X[i])
return result
# ---------------------------------------------------------
def best_split(self, rows): # Extra Trees version
best_col_idx = -1
best_thresh = 0.0
best_var = float('inf')
n_rows = len(rows)
n_cols = len(self.train_X[0])
# Fisher-Yates shuffle to get candidate features
col_indices = np.arange(n_cols)
for i in range(n_cols - 1):
ri = self.rnd.randint(i, n_cols)
tmp = col_indices[i]
col_indices[i] = col_indices[ri]
col_indices[ri] = tmp
n_cols_to_use = min(self.n_split_cols, n_cols) \
if self.n_split_cols != -1 else n_cols
active_cols = col_indices[0:n_cols_to_use]
# evaluate a threshold for each active column
for col_idx in active_cols:
feature_vals = self.train_X[rows, col_idx]
min_v = np.min(feature_vals)
max_v = np.max(feature_vals)
# if all feature values are identical,
# this column cannot be split
if min_v == max_v:
continue
# EXTRA TREES MECHANIC:
# select a single threshold completely at random
thresh = self.rnd.uniform(min_v, max_v)
left_count = 0
right_count = 0
left_sum_y = 0.0
left_sum_sq_y = 0.0
# count and sum target values to compute
# variance reduction
for r in rows:
y_curr = self.train_y[r]
if self.train_X[r, col_idx] "lte" thresh:
left_count += 1
left_sum_y += y_curr
left_sum_sq_y += y_curr * y_curr
else:
right_count += 1
# enforce min_leaf boundaries
if left_count "lt" self.min_leaf or \
right_count "lt" self.min_leaf:
continue
# isolate right side aggregates dynamically
# using total sums
total_sum_y = np.sum(self.train_y[rows])
total_sum_sq_y = np.sum(self.train_y[rows] ** 2)
right_sum_y = total_sum_y - left_sum_y
right_sum_sq_y = total_sum_sq_y - left_sum_sq_y
# variance shortcut formula: E[X^2] - (E[X])^2
left_var = (left_sum_sq_y / left_count) - \
((left_sum_y / left_count) ** 2)
right_var = (right_sum_sq_y / right_count) - \
((right_sum_y / right_count) ** 2)
if left_var "lt" 0.0: left_var = 0.0
if right_var "lt" 0.0: right_var = 0.0
weighted_var = ((left_count * left_var) + \
(right_count * right_var)) / n_rows
if weighted_var "lt" best_var:
best_var = weighted_var
best_col_idx = col_idx
best_thresh = thresh
return best_col_idx, best_thresh
# ---------------------------------------------------------
def tree_target_mean(self, rows):
if rows is None or len(rows) == 0: return 0.0
sum = 0.0
for i in range(len(rows)):
r = rows[i]
sum += self.train_y[r]
return sum / len(rows)
# ---------------------------------------------------------
# ===========================================================
# ===========================================================
print("\nExtra trees regression scratch Python NumPy ")
print("\nLoading synthetic train (200), test (40) data ")
train_file = ".\\Data\\synthetic_train_200.txt"
train_X = np.loadtxt(train_file, comments="#",
usecols=[0,1,2,3,4],
delimiter=",", dtype=np.float64)
train_y = np.loadtxt(train_file, comments="#", usecols=5,
delimiter=",", dtype=np.float64)
test_file = ".\\Data\\synthetic_test_40.txt"
test_X = np.loadtxt(test_file, comments="#",
usecols=[0,1,2,3,4],
delimiter=",", dtype=np.float64)
test_y = np.loadtxt(test_file, comments="#", usecols=5,
delimiter=",", dtype=np.float64)
print("Done ")
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])
n_ests = 200
max_d = 6
max_f = 4
print("\nSetting n_estimators = " + str(n_ests))
print("Setting max_depth = " + str(max_d))
print("Setting max_features = " + str(max_f))
model = MyExtraTreesRegressor(n_estimators=n_ests,
max_depth=max_d, min_samples_split=2,
max_features=max_f, RandomState=0)
model.fit(train_X, train_y)
acc_train = accuracy(model, train_X, train_y, 0.10)
print("\nAccuracy on train (within 0.10) = \
%0.4f " % acc_train)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("Accuracy on test (within 0.10) = \
%0.4f " % acc_test)
mse_train = MSE(model, train_X, train_y)
print("\nMSE on train = %0.4f " % mse_train)
mse_test = MSE(model, test_X, test_y)
print("MSE on test = %0.4f " % mse_test)
x = train_X[0].reshape(1,-1)
print("\nPredicting for: ")
print(x)
y_pred = model.predict(x)[0]
print("Predicted y = %0.4f " % y_pred)
# ==== SCIKIT ===========
from sklearn.ensemble import ExtraTreesRegressor
print("\nSCIKIT: ")
model = ExtraTreesRegressor(n_estimators=n_ests,
max_depth=max_d, max_features=max_f, random_state=0)
model.fit(train_X, train_y)
acc_train = accuracy(model, train_X, train_y, 0.10)
print("\nAccuracy on train (within 0.10) = \
%0.4f " % acc_train)
acc_test = accuracy(model, test_X, test_y, 0.10)
print("Accuracy on test (within 0.10) = \
%0.4f " % acc_test)
mse_train = MSE(model, train_X, train_y)
print("\nMSE on train = %0.4f " % mse_train)
mse_test = MSE(model, test_X, test_y)
print("MSE on test = %0.4f " % mse_test)
print("\nDone ")
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
DevIntersection Conference
Machine Learning Week
Ai4 Conference
G2E Conference
iSC West Conference
You must be logged in to post a comment.