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December 4, 2018 13:57
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# -*- coding: utf-8 -*- | |
""" | |
Использование автоматического дифференцирования autograd (https://github.com/HIPS/autograd) | |
для решения линейной регрессии МНК. | |
""" | |
from __future__ import print_function | |
import autograd.numpy as np | |
from autograd import grad | |
n_samples = 50 | |
X_data = np.linspace(1, 50, n_samples).reshape((n_samples, 1)) | |
y_data = 2.0*X_data + 0.3 + 1e-4*np.random.randn(n_samples).reshape((n_samples, 1)) | |
y_data = y_data.reshape((n_samples, 1)) | |
X_data = np.hstack([X_data, np.ones((n_samples, 1))]) | |
def cost(w): | |
pred = np.dot(X_data, w) | |
return np.sqrt(((pred - y_data) ** 2).mean(axis=None)) | |
grad_cost = grad(cost) | |
W = 0.0 | |
b = 0.0 | |
weights = np.array([W, b]).reshape((2, 1)) | |
learning_rate0 = 0.01 | |
learning_rate = learning_rate0 | |
lr_decay = 0.9999 | |
min_lr = 1e-5 | |
tolerance = 1e-2 | |
iter = 0 | |
while True: | |
iter += 1 | |
print("*"*30) | |
print('iteration #{}'.format(iter)) | |
print("*"*30) | |
weights2 = weights - grad_cost(weights)*learning_rate | |
delta_w = weights2[0, 0] - weights[0, 0] | |
delta_b = weights2[1, 0] - weights[1, 0] | |
cur_cost = cost(weights) | |
print('cost={} W={} b={} delta_w={} delta_b={}'.format(cur_cost, weights[0, 0], weights[1, 0], delta_w, delta_b)) | |
weights = weights2 | |
learning_rate = max(min_lr, learning_rate * lr_decay) | |
print('learning_rate={:8.6f}'.format(learning_rate)) | |
if cur_cost <= tolerance: | |
print('Current cost={} is smaller than tolerance={}, optimization complete.'.format(cur_cost, tolerance)) | |
break | |
print('All done.') |
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