Theano Logistic Regression

原理

逻辑回归的推理过程可以参考这篇文章：http://blog.csdn.net/zouxy09/article/details/20319673，其中包含了关于逻辑回归的推理，梯度下降以及python源码，讲的有点多，可以直接看核心部分

对于这篇文章补充一个就是其缺少的正则化内容：
可以查看知乎上的一个回答，算是比较完整
https://www.zhihu.com/question/35508851/answer/63093225

Theano 代码

#!/usr/bin/env python# -*- encoding:utf-8 -*-'''This is done by Vincent.Ymainly modified from deep learning tutorial'''import numpy as npimport theanoimport theano.tensor as Tfrom theano import functionfrom sklearn.datasets import make_moonsimport matplotlib.pyplot as pltclass LogisticRegression():    def __init__(self,X,n_in,n_out):        self.W = theano.shared(            value=np.zeros(                (n_in,n_out),                dtype=theano.config.floatX            ),            name='W',            borrow=True        )        self.b=theano.shared(            value=np.zeros(                (n_out,),                dtype=theano.config.floatX            ),            name='b',            borrow=True        )        self.p_y_given_x=T.nnet.softmax(T.dot(X,self.W)+self.b)        self.y_pred=T.argmax(self.p_y_given_x,axis=1)        self.params=[self.W,self.b]        self.X=X    def negative_log_likelihood(self,y):        return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]),y])    def errors(self,y):        if y.ndim != self.y_pred.ndim:            raise TypeError(                'y should have the same shape as self.y_pred',                ('y',y.type,'y_pred',self.y_pred.type)            )        if y.dtype.startswith('int'):            return T.mean(T.neq(self.y_pred,y))        else:            return NotImplementedError()def load_data():    #we generate data from sklearn    np.random.seed(0)    X, y = make_moons(800, noise=0.20)    print "xxxxx",X.shape    #return train validate test sets     return [(X[0:600,],y[0:600,]),(X[600:800,],y[600:800,])]def sgd_optimization(learing_rate=0.12,n_epochs=300):    datasets=load_data()    train_set_x,train_set_y=datasets[0]    test_set_x,test_set_y=datasets[1]    index=T.lscalar()    x = T.matrix('x')    y = T.lvector('y')    classifier=LogisticRegression(X=x,n_in=2,n_out=2)    cost=classifier.negative_log_likelihood(y)    test_model=function(        inputs=[x,y],        outputs=classifier.errors(y)    )    g_W=T.grad(cost=cost,wrt=classifier.W)    g_b=T.grad(cost=cost,wrt=classifier.b)    updates=[(classifier.W,classifier.W-learing_rate*g_W),        (classifier.b,classifier.b-learing_rate*g_b)]    train_model=function(        inputs=[x,y],        outputs=classifier.errors(y),        updates=updates    )    epoch=0    while(epoch<n_epochs):      epoch=epoch+1      avg_cost=train_model(train_set_x,train_set_y)      test_cost=test_model(test_set_x,test_set_y)      print "epoch is %d,train error %f, test error %f"%(epoch,avg_cost,test_cost)    predict_model=function(        inputs=[x],        outputs=classifier.y_pred        )    plot_decision_boundary(lambda x:predict_model(x),train_set_x,train_set_y)def plot_decision_boundary(pred_func,train_set_x,train_set_y):    x_min, x_max = train_set_x[:, 0].min() - .5, train_set_x[:, 0].max() + .5    y_min, y_max = train_set_x[:, 1].min() - .5, train_set_x[:, 1].max() + .5    h = 0.01    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])    Z = Z.reshape(xx.shape)    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)    plt.scatter(train_set_x[:, 0], train_set_x[:, 1], c=train_set_y, cmap=plt.cm.Spectral)    plt.show()if __name__=="__main__":    sgd_optimization()

效果