Python学习笔记之逻辑回归

 # -*- coding: utf-8 -*-
 """
 Created on Wed Apr 22 17:39:19 2015

 @author: 90Zeng
 """

 import numpy
 import theano
 import theano.tensor as T
 import matplotlib.pyplot as plt
 rng = numpy.random
 N = 400 # 400个样本
 feats = 784 # 每个样本的维度
 D = (rng.randn(N, feats), rng.randint(size=N, low=0, high=2))
 training_steps = 10000

 # Declare Theano symbolic variables
 x = T.dmatrix("x")
 y = T.dvector("y")

 # 随机初始化权重
 w = theano.shared(rng.randn(feats), name="w")
 # 偏置初始化为 0
 b = theano.shared(0.0, name="b")
 print "Initial model:"
 print w.get_value(), b.get_value()

 # Construct Theano expression graph
 p_1 = 1 / (1 + T.exp(-T.dot(x, w) - b))   # Probability that target = 1
 prediction = p_1 > 0.5                    # The prediction thresholded
 xent = -y * T.log(p_1) - (1-y) * T.log(1-p_1) # Cross-entropy loss function
 lost_avg = xent.mean()
 cost = xent.mean() + 0.01 * (w ** 2).sum()# The cost to minimize
 gw, gb = T.grad(cost, [w, b])             # Compute the gradient of the cost
                                           # (we shall return to this in a
                                           # following section of this tutorial)

 # Compile
 train = theano.function(
     inputs=[x,y],
     outputs=[prediction, lost_avg],
     updates=((w, w - 0.1 * gw),(b, b - 0.1 * gb)),
     )
 predict=theano.function(
     inputs=[x],
     outputs=prediction,
     )

 # Train
 err = []
 for i in range(training_steps):
     pred, er = train(D[0], D[1])
     err.append(er)

 print "Final model:"
 print w.get_value(), b.get_value()
 print "target values for D:", D[1]
 print "prediction on D:", predict(D[0])

 # 画出损失函数图
 x = range(1000)
 plt.plot(x,err[0:1000])

损失函数随着迭代次数变化，运行结果：