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simple 1-step gradient descent
# From udacity Machine Learning Nanodegree course
import numpy as np
# Define sigmoid function
def sigmoid(x):
return 1/(1+np.exp(-x))
# Derivative of the sigmoid function
def sigmoid_derivative(x):
return sigmoid(x) * (1 - sigmoid(x))
# Feature data
feature = np.array([0.9, -0.2])
# Label data (Target)
label = 0.9
# Weights of neural network
weights = np.array([0.3, -0.8])
# The learning rate, eta in the weight step equation
learnrate = 0.1
# the linear combination performed by the node (h in f(h) and f'(h))
h = np.dot(feature, weights)
# The neural network output (label-hat)
nn_output = sigmoid(h)
# output error (label - label-hat)
error = label - nn_output
# output gradient (f'(h))
output_grad = sigmoid_derivative(h)
# error term (lowercase delta)
error_term = error * output_grad
# Gradient descent step
del_w = learnrate * error_term * feature
print('Output: %s' % nn_output)
print('Error: %s' % error)
print('Change in Weights: %s' % del_w)
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