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multiclass Logistic Regression
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#!/usr/bin/env python | |
# -*- coding: utf-8 -*- | |
''' | |
Logistic Regression | |
References : | |
- Jason Rennie: Logistic Regression, | |
http://qwone.com/~jason/writing/lr.pdf | |
- DeepLearningTutorials | |
https://github.com/lisa-lab/DeepLearningTutorials | |
''' | |
import sys | |
import numpy | |
numpy.seterr(all='ignore') | |
def sigmoid(x): | |
return 1. / (1 + numpy.exp(-x)) | |
def softmax(x): | |
e = numpy.exp(x - numpy.max(x)) # prevent overflow | |
if e.ndim == 1: | |
return e / numpy.sum(e, axis=0) | |
else: | |
return e / numpy.array([numpy.sum(e, axis=1)]).T # ndim = 2 | |
class LogisticRegression(object): | |
def __init__(self, input, label, n_in, n_out): | |
self.x = input | |
self.y = label | |
self.W = numpy.zeros((n_in, n_out)) # initialize W 0 | |
self.b = numpy.zeros(n_out) # initialize bias 0 | |
# self.params = [self.W, self.b] | |
def train(self, lr=0.1, input=None, L2_reg=0.00): | |
if input is not None: | |
self.x = input | |
# p_y_given_x = sigmoid(numpy.dot(self.x, self.W) + self.b) | |
p_y_given_x = softmax(numpy.dot(self.x, self.W) + self.b) | |
d_y = self.y - p_y_given_x | |
self.W += lr * numpy.dot(self.x.T, d_y) - lr * L2_reg * self.W | |
self.b += lr * numpy.mean(d_y, axis=0) | |
# cost = self.negative_log_likelihood() | |
# return cost | |
def negative_log_likelihood(self): | |
# sigmoid_activation = sigmoid(numpy.dot(self.x, self.W) + self.b) | |
sigmoid_activation = softmax(numpy.dot(self.x, self.W) + self.b) | |
cross_entropy = - numpy.mean( | |
numpy.sum(self.y * numpy.log(sigmoid_activation) + | |
(1 - self.y) * numpy.log(1 - sigmoid_activation), | |
axis=1)) | |
return cross_entropy | |
def predict(self, x): | |
# return sigmoid(numpy.dot(x, self.W) + self.b) | |
return softmax(numpy.dot(x, self.W) + self.b) | |
def test_lr(learning_rate=0.01, n_epochs=200): | |
# training data | |
x = numpy.array([[1,1,1,0,0,0], | |
[1,0,1,0,0,0], | |
[1,1,1,0,0,0], | |
[0,0,1,1,1,0], | |
[0,0,1,1,0,0], | |
[0,0,1,1,1,0]]) | |
y = numpy.array([[1, 0], | |
[1, 0], | |
[1, 0], | |
[0, 1], | |
[0, 1], | |
[0, 1]]) | |
# construct LogisticRegression | |
classifier = LogisticRegression(input=x, label=y, n_in=6, n_out=2) | |
# train | |
for epoch in xrange(n_epochs): | |
classifier.train(lr=learning_rate) | |
cost = classifier.negative_log_likelihood() | |
print >> sys.stderr, 'Training epoch %d, cost is ' % epoch, cost | |
learning_rate *= 0.95 | |
# test | |
x = numpy.array([1, 1, 0, 0, 0, 0]) | |
print >> sys.stderr, classifier.predict(x) | |
if __name__ == "__main__": | |
test_lr() |
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Thanks a lot.