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360 lines
6.1 KiB
Markdown
360 lines
6.1 KiB
Markdown
# Theano 实例：Softmax 回归
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## MNIST 数据集的下载和导入
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[MNIST 数据集](http://yann.lecun.com/exdb/mnist/) 是一个手写数字组成的数据集，现在被当作一个机器学习算法评测的基准数据集。
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这是一个下载并解压数据的脚本：
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In [1]:
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```py
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%%file download_mnist.py
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import os
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import os.path
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import urllib
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import gzip
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import shutil
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if not os.path.exists('mnist'):
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os.mkdir('mnist')
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def download_and_gzip(name):
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if not os.path.exists(name + '.gz'):
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urllib.urlretrieve('http://yann.lecun.com/exdb/' + name + '.gz', name + '.gz')
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if not os.path.exists(name):
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with gzip.open(name + '.gz', 'rb') as f_in, open(name, 'wb') as f_out:
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shutil.copyfileobj(f_in, f_out)
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download_and_gzip('mnist/train-images-idx3-ubyte')
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download_and_gzip('mnist/train-labels-idx1-ubyte')
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download_and_gzip('mnist/t10k-images-idx3-ubyte')
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download_and_gzip('mnist/t10k-labels-idx1-ubyte')
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```
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```py
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Overwriting download_mnist.py
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```
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可以运行这个脚本来下载和解压数据：
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In [2]:
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```py
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%run download_mnist.py
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```
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使用如下的脚本来导入 MNIST 数据，源码地址：
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[https://github.com/Newmu/Theano-Tutorials/blob/master/load.py](https://github.com/Newmu/Theano-Tutorials/blob/master/load.py)
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In [3]:
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```py
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%%file load.py
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import numpy as np
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import os
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datasets_dir = './'
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def one_hot(x,n):
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if type(x) == list:
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x = np.array(x)
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x = x.flatten()
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o_h = np.zeros((len(x),n))
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o_h[np.arange(len(x)),x] = 1
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return o_h
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def mnist(ntrain=60000,ntest=10000,onehot=True):
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data_dir = os.path.join(datasets_dir,'mnist/')
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fd = open(os.path.join(data_dir,'train-images-idx3-ubyte'))
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loaded = np.fromfile(file=fd,dtype=np.uint8)
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trX = loaded[16:].reshape((60000,28*28)).astype(float)
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fd = open(os.path.join(data_dir,'train-labels-idx1-ubyte'))
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loaded = np.fromfile(file=fd,dtype=np.uint8)
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trY = loaded[8:].reshape((60000))
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fd = open(os.path.join(data_dir,'t10k-images-idx3-ubyte'))
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loaded = np.fromfile(file=fd,dtype=np.uint8)
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teX = loaded[16:].reshape((10000,28*28)).astype(float)
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fd = open(os.path.join(data_dir,'t10k-labels-idx1-ubyte'))
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loaded = np.fromfile(file=fd,dtype=np.uint8)
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teY = loaded[8:].reshape((10000))
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trX = trX/255.
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teX = teX/255.
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trX = trX[:ntrain]
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trY = trY[:ntrain]
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teX = teX[:ntest]
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teY = teY[:ntest]
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if onehot:
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trY = one_hot(trY, 10)
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teY = one_hot(teY, 10)
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else:
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trY = np.asarray(trY)
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teY = np.asarray(teY)
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return trX,teX,trY,teY
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```
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```py
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Overwriting load.py
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```
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## softmax 回归
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`Softmax` 回归相当于 `Logistic` 回归的一个一般化，`Logistic` 回归处理的是两类问题，`Softmax` 回归处理的是 `N` 类问题。
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`Logistic` 回归输出的是标签为 1 的概率（标签为 0 的概率也就知道了），对应地，对 N 类问题 `Softmax` 输出的是每个类对应的概率。
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具体的内容，可以参考 `UFLDL` 教程：
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[http://ufldl.stanford.edu/wiki/index.php/Softmax%E5%9B%9E%E5%BD%92](http://ufldl.stanford.edu/wiki/index.php/Softmax%E5%9B%9E%E5%BD%92)
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In [4]:
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```py
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import theano
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from theano import tensor as T
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import numpy as np
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from load import mnist
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```
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```py
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Using gpu device 1: Tesla C2075 (CNMeM is disabled)
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```
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我们来看它具体的实现。
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这两个函数一个是将数据转化为 `GPU` 计算的类型，另一个是初始化权重：
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In [5]:
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```py
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def floatX(X):
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return np.asarray(X, dtype=theano.config.floatX)
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def init_weights(shape):
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return theano.shared(floatX(np.random.randn(*shape) * 0.01))
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```
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`Softmax` 的模型在 `theano` 中已经实现好了：
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In [6]:
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```py
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A = T.matrix()
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B = T.nnet.softmax(A)
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test_softmax = theano.function([A], B)
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a = floatX(np.random.rand(3, 4))
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b = test_softmax(a)
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print b.shape
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# 行和
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print b.sum(1)
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```
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```py
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(3, 4)
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[ 1.00000012 1\. 1\. ]
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```
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`softmax` 函数会按照行对矩阵进行 `Softmax` 归一化。
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所以我们的模型为：
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In [7]:
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```py
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def model(X, w):
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return T.nnet.softmax(T.dot(X, w))
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```
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导入数据：
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In [8]:
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```py
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trX, teX, trY, teY = mnist(onehot=True)
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```
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定义变量，并初始化权重：
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In [9]:
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```py
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X = T.fmatrix()
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Y = T.fmatrix()
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w = init_weights((784, 10))
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```
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定义模型输出和预测：
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In [10]:
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```py
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py_x = model(X, w)
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y_pred = T.argmax(py_x, axis=1)
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```
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损失函数为多类的交叉熵，这个在 `theano` 中也被定义好了：
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In [11]:
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```py
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cost = T.mean(T.nnet.categorical_crossentropy(py_x, Y))
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gradient = T.grad(cost=cost, wrt=w)
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update = [[w, w - gradient * 0.05]]
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```
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编译 `train` 和 `predict` 函数：
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In [12]:
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```py
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train = theano.function(inputs=[X, Y], outputs=cost, updates=update, allow_input_downcast=True)
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predict = theano.function(inputs=[X], outputs=y_pred, allow_input_downcast=True)
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```
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迭代 100 次，测试集正确率为 0.925：
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In [13]:
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```py
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for i in range(100):
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for start, end in zip(range(0, len(trX), 128), range(128, len(trX), 128)):
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cost = train(trX[start:end], trY[start:end])
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print "{0:03d}".format(i), np.mean(np.argmax(teY, axis=1) == predict(teX))
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```
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```py
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``` |