用Theano学习Deep Learning（三）：卷积神经网络

题目是CNN，但是CNN的具体原理和之后会写一篇博客在deeplearning目录下详细说明。

简单地说，CNN与NN相比独特之处在于用部分连接代替全链接，并用pooling来对数据进行降维，这样做有几个好处：

对于大图像来说所需训练的参数大大减少
获取图像的部分特征而非全局特征
pooling使得网络的输出结果具有一定的平移和遮挡不变性
demo见：（效果还是挺好的，当年华尔街银行用来读支票）

这里主要说代码。

1、类：LeNetConvPoolLayer

包括了一次卷积和一次pooling，一共两层。
初始化参数输入数据，输入图片大小，卷积核大小，池化大小
池化并不使用平均值，而是使用最大值作为输出
中间参数有卷积核W，偏置b，卷积输出和偏置输出，整体输出=tanh（池化输出+偏置）
W和b合并成一个列表params

2、类：evaluate_lenet5

包括了两个LeNetConvPoolLayer（Layer0，1）和两层神经网络（Layer2，3）
第一层神经节点用类：HiddentLayer，第二层用类：OutputLayer（MLP中的内容，以后补）
test_model和validate_model：输入一个样本，输出与label的误差
四层的函数并在一起：params = layer3.params + layer2.params + layer1.params + layer0.params（可以这样？没见过），用grads = T.grad(cost, params)求偏导，好方便。
train_model中用update功能更新参数（更快，update表用for循环构建）

用到的两个类大概就是这个样子。

训练过程中的要点：

两层循环，一层逐个样本训练，参数minibatch_index；一层循环训练总样本，参数epoch；iter表示已经学习次数
参数patience表示最大iter数，初始化维10000，若在评价中发现训练表现良好则翻倍
每到validation_frequency则评价一次，若当前误差比最好误差好0.995则翻倍patience
iter>=patience || epochs>=n_epoch 则停止训练

训练过程大概就是这个样子。

一点感想：

这次一段代码看下来，对python的class有了更深的理解。
就目前的理解，第一次调用class，class会自动初始化里面的参数；
以后每次调用class的函数，class都会自动从头跑一次，更新里面的参数并输出给function
所以一个class is better than c里面的一个function（因为c里面只能计算，而python里面把结构搭建起来了而且保存参数）

Theano.tensor下的shape[]和dimshuffle[]具体用法还不懂
另外这个代码下多处用到了for循环，matlab里面是很忌讳for的。为什么这里却很常用，反而少见矩阵运算了？
validation_losses = [validate_model(i) for i in xrange(n_valid_batches)] 用法很高级
params = layer3.params + layer2.params + layer1.params + layer0.params 是合并表的意思？
用update来更新参数，快准狠！

下面是自己自己一行一行读代码写并写上的中文注释。

This implementation simplifies the model in the following ways:- LeNetConvPool doesn't implement location-specific gain and bias parameters- LeNetConvPool doesn't implement pooling by average, it implements poolingby max.- Digit classification is implemented with a logistic regression rather thanan RBF network- LeNet5 was not fully-connected convolutions at second layer
"""
import cPickle
import gzip
import os
import sys
import time
import numpy
import theano
import theano.tensor as T
from theano.tensor.signal import downsample
from theano.tensor.nnet import conv
from logistic_sgd import LogisticRegression, load_data
from mlp import HiddenLayerclass LeNetConvPoolLayer(object):"""Pool Layer of a convolutional network """def __init__(self, rng, input, filter_shape, image_shape, poolsize=(2, 2)):"""Allocate a LeNetConvPoolLayer with shared variable internal parameters.:type rng: numpy.random.RandomState:param rng: a random number generator used to initialize weights:type input: theano.tensor.dtensor4:param input: symbolic image tensor, of shape image_shape:type filter_shape: tuple or list of length 4:param filter_shape: (number of filters, num input feature maps,filter height,filter width):type image_shape: tuple or list of length 4:param image_shape: (batch size, num input feature maps,image height, image width):type poolsize: tuple or list of length 2:param poolsize: the downsampling (pooling) factor (#rows,#cols)"""assert image_shape[1] == filter_shape[1]self.input = input# there are "num input feature maps * filter height * filter width"# inputs to each hidden unitfan_in = numpy.prod(filter_shape[1:])# each unit in the lower layer receives a gradient from:# "num output feature maps * filter height * filter width" /#   pooling sizefan_out = (filter_shape[0] * numpy.prod(filter_shape[2:]) /numpy.prod(poolsize))# initialize weights with random weightsW_bound = numpy.sqrt(6. / (fan_in + fan_out))self.W = theano.shared(numpy.asarray(rng.uniform(low=-W_bound, high=W_bound, size=filter_shape),dtype=theano.config.floatX),borrow=True)# the bias is a 1D tensor -- one bias per output feature mapb_values = numpy.zeros((filter_shape[0],), dtype=theano.config.floatX)          self.b = theano.shared(value=b_values, borrow=True)# convolve input feature maps with filtersconv_out = conv.conv2d(input=input, filters=self.W,                             #卷积函数，用W卷积不加偏置filter_shape=filter_shape, image_shape=image_shape)# downsample each feature map individually, using maxpoolingpooled_out = downsample.max_pool_2d(input=conv_out,                             #pooling，用max不用mean，不重叠ds=poolsize, ignore_border=True)# add the bias term. Since the bias is a vector (1D array), we first# reshape it to a tensor of shape (1,n_filters,1,1). Each bias will# thus be broadcasted across mini-batches and feature map# width & heightself.output = T.tanh(pooled_out + self.b.dimshuffle('x', 0, 'x', 'x'))          #卷积层池化后加上偏置用tanh输出，dimshuffle()将向量整形为矩阵，具体不懂# store parameters of this layerself.params = [self.W, self.b]                                                  #卷积核+偏置并为参数#学习率=0.1， 学习次数=200， nkerns=[20,50]表示第一层20个核，第二层50个核； 补丁大小：500？？？？
def evaluate_lenet5(learning_rate=0.1, n_epochs=200,                                  dataset='../data/mnist.pkl.gz',nkerns=[20, 50], batch_size=500):""" Demonstrates lenet on MNIST datasets:type learning_rate: float:param learning_rate: learning rate used (factor for the stochasticgradient):type n_epochs: int:param n_epochs: maximal number of epochs to run the optimizer:type dataset: string:param dataset: path to the dataset used for training /testing (MNIST here):type nkerns: list of ints:param nkerns: number of kernels on each layer"""rng = numpy.random.RandomState(23455)                                               #随机数做种datasets = load_data(dataset)                                                       #读入数据train_set_x, train_set_y = datasets[0]                                              #传递三部分数据（解包）valid_set_x, valid_set_y = datasets[1]test_set_x, test_set_y = datasets[2]# compute number of minibatches for training, validation and testing                #表示数据可以借用提高GPU运算速率，shape[0],作用为止n_train_batches = train_set_x.get_value(borrow=True).shape[0]n_valid_batches = valid_set_x.get_value(borrow=True).shape[0]n_test_batches = test_set_x.get_value(borrow=True).shape[0]n_train_batches /= batch_size                                                       #样本总数量n_valid_batches /= batch_sizen_test_batches /= batch_size# allocate symbolic variables for the dataindex = T.lscalar()  # index to a [mini]batch                                       #当前batch的下标x = T.matrix('x')   # the data is presented as rasterized images                    #当前batchy = T.ivector('y')  # the labels are presented as 1D vector of                      #当前batch的标签# [int] labelsishape = (28, 28)  # this is the size of MNIST images####################### BUILD ACTUAL MODEL #######################print '... building the model'# Reshape matrix of rasterized images of shape (batch_size,28*28)# to a 4D tensor, compatible with our LeNetConvPoolLayerlayer0_input = x.reshape((batch_size, 1, 28, 28))                                   #input是reshape的x# Construct the first convolutional pooling layer:# filtering reduces the image size to (28-5+1,28-5+1)=(24,24)# maxpooling reduces this further to (24/2,24/2) = (12,12)# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)#初始化第一个卷积池化layer，input = layer0_inputlayer0 = LeNetConvPoolLayer(rng, input=layer0_input,image_shape=(batch_size, 1, 28, 28),filter_shape=(nkerns[0], 1, 5, 5), poolsize=(2, 2))# Construct the second convolutional pooling layer# filtering reduces the image size to (12-5+1,12-5+1)=(8,8)# maxpooling reduces this further to (8/2,8/2) = (4,4)# 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)#初始化第二个卷积池化layer , input = layer0_outputlayer1 = LeNetConvPoolLayer(rng, input=layer0.output,image_shape=(batch_size, nkerns[0], 12, 12),filter_shape=(nkerns[1], nkerns[0], 5, 5), poolsize=(2, 2))# the TanhLayer being fully-connected, it operates on 2D matrices of# shape (batch_size,num_pixels) (i.e matrix of rasterized images).# This will generate a matrix of shape (20,32*4*4) = (20,512)#layer2是第一层全连接层，拉平后的池化层作为输入layer2_input = layer1.output.flatten(2)# construct a fully-connected sigmoidal layer# 用隐藏层的类表示layer2 = HiddenLayer(rng, input=layer2_input, n_in=nkerns[1] * 4 * 4,n_out=500, activation=T.tanh)# classify the values of the fully-connected sigmoidal layer# 输出是逻辑回归层layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)# the cost we minimize during training is the NLL of the model# 代价函数值用negative_log_likelihood来算，（自带的？）cost = layer3.negative_log_likelihood(y)# create a function to compute the mistakes that are made by the model# 定义一个函数，计算输出层的误差，用givens来覆盖全局变量test_model = theano.function([index], layer3.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]})## 同上定义一个函数，计算输出层的误差，用givens来覆盖全局变量validate_model = theano.function([index], layer3.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]})# create a list of all model parameters to be fit by gradient descent# 各层参数合并params = layer3.params + layer2.params + layer1.params + layer0.params# create a list of gradients for all model parameters# 利用自带的函数计算各参数的偏导grads = T.grad(cost, params)# train_model is a function that updates the model parameters by# SGD Since this model has many parameters, it would be tedious to# manually create an update rule for each model parameter. We thus# create the updates list by automatically looping over all# (params[i],grads[i]) pairs.# 更新参数十分麻烦， 创建一个叫做updates的list来自动更新（？为什么要用for，这样不会很慢吗？——坟蛋这不是matlab！）updates = []for param_i, grad_i in zip(params, grads):updates.append((param_i, param_i - learning_rate * grad_i))# 定义训练函数，输出cost并用update 的方法更新参数train_model = theano.function([index], 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]})################ TRAIN MODEL ################print '... training'# early-stopping parameters                                          patience = 10000  # look as this many examples regardless patience_increase = 2  # wait this much longer when a new best is  如果训练误差良好的话训练的次数变为两倍# foundimprovement_threshold = 0.995  # a relative improvement of this much is 如果误差小于上一次误差的0.995，patience increase# considered significantvalidation_frequency = min(n_train_batches, patience / 2)  #评价训练效果的频率，这个数值为什么这么取我不清楚# go through this manually# minibatche before checking the network# on the validation set; in this case we# check every epochbest_params = Nonebest_validation_loss = numpy.infbest_iter = 0test_score = 0.start_time = time.clock()epoch = 0done_looping = Falsewhile (epoch < n_epochs) and (not done_looping):                        #总体样本训练次数epoch = epoch + 1for minibatch_index in xrange(n_train_batches):                     #逐个样本训练iter = (epoch - 1) * n_train_batches + minibatch_index          #到目前为止总的训练次数if iter % 100 == 0:                                             #每训练100次输出一个提示，提示训练次数print 'training @ iter = ', itercost_ij = train_model(minibatch_index)                          #训练一次if (iter + 1) % validation_frequency == 0:                      #到达需要进行一次评价的次数，对学习结果进行评价# compute zero-one loss on validation set                   #利用for循环和validation_modle(index)返回所有评价样本的误差值并构造一个表validation_losses = [validate_model(i) for iin xrange(n_valid_batches)]this_validation_loss = numpy.mean(validation_losses)        #当前误差值=当前平均print('epoch %i, minibatch %i/%i, validation error %f %%' % \(epoch, minibatch_index + 1, n_train_batches, \this_validation_loss * 100.))# if we got the best validation score until nowif this_validation_loss < best_validation_loss:             #如果当 前平均误差<(最好误差*阀值)，证明参数还有很大的优化空间，加倍训练次数#improve patience if loss improvement is good enoughif this_validation_loss < best_validation_loss *  \improvement_threshold:patience = max(patience, iter * patience_increase)# save best validation score and iteration numberbest_validation_loss = this_validation_lossbest_iter = iter# test it on the test settest_losses = [test_model(i) for i in xrange(n_test_batches)]  #用测试样本对模型参数进行评价test_score = numpy.mean(test_losses)                           #这里有个tip：应为参数使用train集合训练使用validation集合进行评价；print(('     epoch %i, minibatch %i/%i, test error of best '   #所以参数的拟合是会偏向那两个集合的特征的，所以要是用全新的集合来得到参数的客观表现'model %f %%') %                                        #在各种训练中，样本都要分为训练样本、评价(拟合)样本和测试样本进行使用，比例大概是6:2:2，这里是 5:1:1(epoch, minibatch_index + 1, n_train_batches,test_score * 100.))if patience <= iter:                                               #如果没耐性了（到达最大训练次数），就停止训练done_looping = Truebreak#下面就是计时啊评价啊什么什么的end_time = time.clock()print('Optimization complete.')print('Best validation score of %f %% obtained at iteration %i,'\'with test performance %f %%' %(best_validation_loss * 100., best_iter + 1, test_score * 100.))print >> sys.stderr, ('The code for file ' +os.path.split(__file__)[1] +' ran for %.2fm' % ((end_time - start_time) / 60.))
if __name__ == '__main__':evaluate_lenet5()def experiment(state, channel):evaluate_lenet5(state.learning_rate, dataset=state.dataset)

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