首先PO上主要Python代码(2.7), 这个代码在Deep Learning上可以找到.
1 # allocate symbolic variables for the data
2 index = T.lscalar() # index to a [mini]batch
3 x = T.matrix('x') # the data is presented as rasterized images
4 y = T.ivector('y') # the labels are presented as 1D vector of
5 # [int] labels
6
7 # construct the logistic regression class
8 # Each MNIST image has size 28*28
9 classifier = LogisticRegression(input=x, n_in=24 * 48, n_out=10)
10
11 # the cost we minimize during training is the negative log likelihood of
12 # the model in symbolic format
13 cost = classifier.negative_log_likelihood(y)
14
15 # compiling a Theano function that computes the mistakes that are made by
16 # the model on a minibatch
17 test_model = theano.function(inputs=[index],
18 outputs=classifier.errors(y),
19 givens={
20 x: test_set_x[index * batch_size: (index + 1) * batch_size],
21 y: test_set_y[index * batch_size: (index + 1) * batch_size]})
22
23 validate_model = theano.function(inputs=[index],
24 outputs=classifier.errors(y),
25 givens={
26 x: valid_set_x[index * batch_size:(index + 1) * batch_size],
27 y: valid_set_y[index * batch_size:(index + 1) * batch_size]})
28
29 # compute the gradient of cost with respect to theta = (W,b)
30 g_W = T.grad(cost=cost, wrt=classifier.W)
31 g_b = T.grad(cost=cost, wrt=classifier.b)
32
33 # specify how to update the parameters of the model as a list of
34 # (variable, update expression) pairs.
35 updates = [(classifier.W, classifier.W - learning_rate * g_W),
36 (classifier.b, classifier.b - learning_rate * g_b)]
37
38 # compiling a Theano function `train_model` that returns the cost, but in
39 # the same time updates the parameter of the model based on the rules
40 # defined in `updates`
41 train_model = theano.function(inputs=[index],
42 outputs=cost,
43 updates=updates,
44 givens={
45 x: train_set_x[index * batch_size:(index + 1) * batch_size],
46 y: train_set_y[index * batch_size:(index + 1) * batch_size]})
代码长度不算太长, 只是逻辑关系需要厘清. 下面逐行分析这些代码.
代码中的T是theano.tensor的代名词.
行1~行13:
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
x = T.matrix('x') # the data is presented as rasterized images
y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
# construct the logistic regression class
# Each MNIST image has size 28*28
classifier = LogisticRegression(input=x, n_in=24 * 48, n_out=10)
# the cost we minimize during training is the negative log likelihood of
# the model in symbolic format
cost = classifier.negative_log_likelihood(y)
声明index, x, y三个符号变量(类似Matlab的symbol), 分别用来指代训练样本批序号, 输入图像矩阵, 期望输出向量.
classifier是一个LR对象, 调用LR类的构造函数, 并将符号变量x作为输入, 我们就可以使用Theano.function方法在x和classifier中构造联系, 当x改变时, classifier也会改变.
cost指代classifier中的负对数相似度, 使用符号变量y作为输入, 此处的作用和classifier相同, 不再赘述.
行14~行28:
# compiling a Theano function that computes the mistakes that are made by
# the model on a minibatch
test_model = theano.function(inputs=[index],
outputs=classifier.errors(y),
givens={
x: test_set_x[index * batch_size: (index + 1) * batch_size],
y: test_set_y[index * batch_size: (index + 1) * batch_size]})
validate_model = theano.function(inputs=[index],
outputs=classifier.errors(y),
givens={
x: valid_set_x[index * batch_size:(index + 1) * batch_size],
y: valid_set_y[index * batch_size:(index + 1) * batch_size]})
这里的2个model是容易让人迷惑的地方, 关于theano.function, 需要一些基础知识:
比如声明2个符号变量a, b: a, b = T.iscalar(), T.iscalar() , 它们都是整形(i)标量(scalar), 再声明一个变量c: c = a + b , 我们通过type(c)来查看其类型:
>>> type(c) <class 'theano.tensor.var.TensorVariable'> >>> type(a) <class 'theano.tensor.var.TensorVariable'>
c的类型和a, b相同, 都是Tensor变量. 至此准备工作完成, 我们通过theano.function来构建关系: add = theano.function(inputs = [a, b], output = c) . 这条语句就构造了一个函数add, 它接收a, b为输入, 输出为c. 我们在Python中这样使用它即可:
>>> add = theano.function(inputs = [a, b], outputs = c) >>> test = add(100, 100) >>> test array(200)
好了, 有了基础知识, 就可以理解这2个model的含义:
test_model = theano.function(inputs=[index],
outputs=classifier.errors(y),
givens={
x: test_set_x[index * batch_size: (index + 1) * batch_size],
y: test_set_y[index * batch_size: (index + 1) * batch_size]})
输入是index, 输出则是classifier对象中的errors方法的返回值, 其中y作为errors方法的输入参数. 其中的classifier接收x作为输入参数.
givens关键字的作用是使用冒号后面的变量来替代冒号前面的变量, 本例中, 即使用测试数据中的第index批数据(一批有batch_size个)来替换x和y.
test_model用中文来解释就是: 接收第index批测试数据的图像数据x和期望输出y作为输入, 返回误差值的函数.
validate_model = theano.function(inputs=[index],
outputs=classifier.errors(y),
givens={
x: valid_set_x[index * batch_size:(index + 1) * batch_size],
y: valid_set_y[index * batch_size:(index + 1) * batch_size]})
这里同上, 只不过使用的是验证数据.
行29~行32:
# compute the gradient of cost with respect to theta = (W,b)
g_W = T.grad(cost=cost, wrt=classifier.W)
g_b = T.grad(cost=cost, wrt=classifier.b)
计算的是梯度, 用于学习算法, T.grad(y, x) 计算的是相对于x的y的梯度.
行33~行37:
# specify how to update the parameters of the model as a list of
# (variable, update expression) pairs.
updates = [(classifier.W, classifier.W - learning_rate * g_W),
(classifier.b, classifier.b - learning_rate * g_b)]
updates是一个长度为2的list, 每个元素都是一组tuple, 在theano.function中, 每次调用对应函数, 使用tuple中的第二个元素来更新第一个元素.
行38~行46:
# compiling a Theano function `train_model` that returns the cost, but in
# the same time updates the parameter of the model based on the rules
# defined in `updates`
train_model = theano.function(inputs=[index],
outputs=cost,
updates=updates,
givens={
x: train_set_x[index * batch_size:(index + 1) * batch_size],
y: train_set_y[index * batch_size:(index + 1) * batch_size]})
这里其余部分不再赘述. 需要注意的是增加了一个updates参数, 这个参数给定了每次调用train_model时对某些参数的修改(W, b). 另外输出也变成了cost函数(对数误差)而非test_model和valid-model中的errors函数(绝对误差).