用Theano学习Deep Learning（三）：卷积神经网络
写在前面的废话：
出了托福成绩啦，本人战战兢兢考了个97！成绩好的出乎意料！喜大普奔！撒花庆祝！
傻…………寒假还要怒学一个月刷100庆祝个毛线…………
正题：
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
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- 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
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- 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？
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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。（cnblog太窄复制到文本编辑器看吧，推荐sublime）
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 pooling by max. - Digit classification is implemented with a logistic regression rather than an 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 HiddenLayer class 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 unit fan_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 size fan_out = (filter_shape[0] * numpy.prod(filter_shape[2:]) / numpy.prod(poolsize)) # initialize weights with random weights W_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 map b_values = numpy.zeros((filter_shape[0],), dtype=theano.config.floatX) self.b = theano.shared(value=b_values, borrow=True) # convolve input feature maps with filters conv_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 maxpooling pooled_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 & height self.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 layer self.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 stochastic gradient) :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_size n_test_batches /= batch_size # allocate symbolic variables for the data index = 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batch y = T.ivector('y') # the labels are presented as 1D vector of #当前batch的标签 # [int] labels ishape = (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 LeNetConvPoolLayer layer0_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_input layer0 = 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_output layer1 = 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 # found improvement_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 significant validation_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 epoch best_params = None best_validation_loss = numpy.inf best_iter = 0 test_score = 0. start_time = time.clock() epoch = 0 done_looping = False while (epoch < n_epochs) and (not done_looping): #总体样本训练次数 epoch = epoch + 1 for 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 = ', iter cost_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 i in 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 now if 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 enough if this_validation_loss < best_validation_loss * \ improvement_threshold: patience = max(patience, iter * patience_increase) # save best validation score and iteration number best_validation_loss = this_validation_loss best_iter = iter # test it on the test set test_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 = True break #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)
