机器学习|PyTorch简明教程下篇

接着上篇《PyTorch简明教程上篇》，继续学习多层感知机，卷积神经网络和LSTMNet。

1、多层感知机

多层感知机是一种简单的神经网络，也是深度学习的重要基础。它通过在网络中添加一个或多个隐藏层来克服线性模型的限制。具体的图示如下：

import numpy as npimport torchfrom torch.autograd import Variablefrom torch import optimfrom data_util import load_mnistdef build_model(input_dim, output_dim):return torch.nn.Sequential(torch.nn.Linear(input_dim, 512, bias=False),torch.nn.ReLU(),torch.nn.Dropout(0.2),torch.nn.Linear(512, 512, bias=False),torch.nn.ReLU(),torch.nn.Dropout(0.2),torch.nn.Linear(512, output_dim, bias=False),)def train(model, loss, optimizer, x_val, y_val):model.train()optimizer.zero_grad()fx = model.forward(x_val)output = loss.forward(fx, y_val)output.backward()optimizer.step()return output.item()def predict(model, x_val):model.eval()output = model.forward(x_val)return output.data.numpy().argmax(axis=1)def main():torch.manual_seed(42)trX, teX, trY, teY = load_mnist(notallow=False)trX = torch.from_numpy(trX).float()teX = torch.from_numpy(teX).float()trY = torch.tensor(trY)n_examples, n_features = trX.size()n_classes = 10model = build_model(n_features, n_classes)loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')optimizer = optim.Adam(model.parameters())batch_size = 100for i in range(100):cost = 0.num_batches = n_examples // batch_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += train(model, loss, optimizer,trX[start:end], trY[start:end])predY = predict(model, teX)print("Epoch %d, cost = %f, acc = %.2f%%"% (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))if __name__ == "__main__":main()

（1）以上代码和单层神经网络的代码类似，区别是build_model构建一个包含三个线性层和两个ReLU激活函数的神经网络模型：

• 向模型中添加第一个线性层，该层的输入特征数量为input_dim，输出特征数量为512；
• 接着添加一个ReLU激活函数和一个Dropout层，用于增强模型的非线性能力和防止过拟合；
• 向模型中添加第二个线性层，该层的输入特征数量为512，输出特征数量为512；
• 接着添加一个ReLU激活函数和一个Dropout层；
• 向模型中添加第三个线性层，该层的输入特征数量为512，输出特征数量为output_dim，即模型的输出类别数量；

（2）什么是ReLU激活函数？ReLU（Rectified Linear Unit，修正线性单元）激活函数是深度学习和神经网络中常用的一种激活函数，ReLU函数的数学表达式为：f(x) = max(0, x)，其中x是输入值。ReLU函数的特点是当输入值小于等于0时，输出为0；当输入值大于0时，输出等于输入值。简单来说，ReLU函数就是将负数部分抑制为0，正数部分保持不变。ReLU激活函数在神经网络中的作用是引入非线性因素，使得神经网络能够拟合复杂的非线性关系，同时，ReLU函数相对于其他激活函数（如Sigmoid或Tanh）具有计算速度快、收敛速度快等优点；

（3）什么是Dropout层？Dropout层是一种在神经网络中用于防止过拟合的技术。在训练过程中，Dropout层会随机地将一部分神经元的输出置为0，即"丢弃"这些神经元，这样做的目的是为了减少神经元之间的相互依赖，从而提高网络的泛化能力；

（4）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印当前训练的轮次，损失值和acc，上述的代码输出如下：

...Epoch 91, cost = 0.011129, acc = 98.45%Epoch 92, cost = 0.007644, acc = 98.58%Epoch 93, cost = 0.011872, acc = 98.61%Epoch 94, cost = 0.010658, acc = 98.58%Epoch 95, cost = 0.007274, acc = 98.54%Epoch 96, cost = 0.008183, acc = 98.43%Epoch 97, cost = 0.009999, acc = 98.33%Epoch 98, cost = 0.011613, acc = 98.36%Epoch 99, cost = 0.007391, acc = 98.51%Epoch 100, cost = 0.011122, acc = 98.59%

可以看出最后相同的数据分类，准确率比单层神经网络要高（98.59% > 97.68%）。

2、卷积神经网络

卷积神经网络（CNN）是一种深度学习算法。当输入一个矩阵时，CNN可以对其中的重要和不重要部分进行区分（分配权重）。相较于其他分类任务，CNN对数据预处理的要求并不高，只要经过充分的训练，就能够学习到矩阵的特征。下图展示了该过程：

import numpy as npimport torchfrom torch.autograd import Variablefrom torch import optimfrom data_util import load_mnistclass ConvNet(torch.nn.Module):def __init__(self, output_dim):super(ConvNet, self).__init__()self.conv = torch.nn.Sequential()self.conv.add_module("conv_1", torch.nn.Conv2d(1, 10, kernel_size=5))self.conv.add_module("maxpool_1", torch.nn.MaxPool2d(kernel_size=2))self.conv.add_module("relu_1", torch.nn.ReLU())self.conv.add_module("conv_2", torch.nn.Conv2d(10, 20, kernel_size=5))self.conv.add_module("dropout_2", torch.nn.Dropout())self.conv.add_module("maxpool_2", torch.nn.MaxPool2d(kernel_size=2))self.conv.add_module("relu_2", torch.nn.ReLU())self.fc = torch.nn.Sequential()self.fc.add_module("fc1", torch.nn.Linear(320, 50))self.fc.add_module("relu_3", torch.nn.ReLU())self.fc.add_module("dropout_3", torch.nn.Dropout())self.fc.add_module("fc2", torch.nn.Linear(50, output_dim))def forward(self, x):x = self.conv.forward(x)x = x.view(-1, 320)return self.fc.forward(x)def train(model, loss, optimizer, x_val, y_val):model.train()optimizer.zero_grad()fx = model.forward(x_val)output = loss.forward(fx, y_val)output.backward()optimizer.step()return output.item()def predict(model, x_val):model.eval()output = model.forward(x_val)return output.data.numpy().argmax(axis=1)def main():torch.manual_seed(42)trX, teX, trY, teY = load_mnist(notallow=False)trX = trX.reshape(-1, 1, 28, 28)teX = teX.reshape(-1, 1, 28, 28)trX = torch.from_numpy(trX).float()teX = torch.from_numpy(teX).float()trY = torch.tensor(trY)n_examples = len(trX)n_classes = 10model = ConvNet(output_dim=n_classes)loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)batch_size = 100for i in range(100):cost = 0.num_batches = n_examples // batch_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += train(model, loss, optimizer,trX[start:end], trY[start:end])predY = predict(model, teX)print("Epoch %d, cost = %f, acc = %.2f%%"% (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))if __name__ == "__main__":main()

（1）以上代码定义了一个名为ConvNet的类，它继承自torch.nn.Module类，表示一个卷积神经网络，在__init__方法中定义了两个子模块conv和fc，分别表示卷积层和全连接层。在conv子模块中，我们定义了两个卷积层（torch.nn.Conv2d）、两个最大池化层（torch.nn.MaxPool2d）、两个ReLU激活函数（torch.nn.ReLU）和一个Dropout层（torch.nn.Dropout）。在fc子模块中，定义了两个线性层（torch.nn.Linear）、一个ReLU激活函数和一个Dropout层；

池化层在CNN中扮演着重要的角色，其主要目的有以下几点：

• 降低维度：池化层通过对输入特征图（Feature maps）进行局部区域的下采样操作，降低了特征图的尺寸。这样可以减少后续层中的参数数量，降低计算复杂度，加速训练过程；
• 平移不变性：池化层可以提高网络对输入图像的平移不变性。当图像中的某个特征发生小幅度平移时，池化层的输出仍然具有相似的特征表示。这有助于提高模型的泛化能力，使其能够在不同位置和尺度下识别相同的特征；
• 防止过拟合：通过减少特征图的尺寸，池化层可以降低模型的参数数量，从而降低过拟合的风险；
• 增强特征表达：池化操作可以聚合局部区域内的特征，从而强化和突出更重要的特征信息。常见的池化操作有最大池化（Max Pooling）和平均池化（Average Pooling），分别表示在局部区域内取最大值或平均值作为输出；

（3）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印当前训练的轮次，损失值和acc，上述的代码输出如下：

...Epoch 91, cost = 0.047302, acc = 99.22%Epoch 92, cost = 0.049026, acc = 99.22%Epoch 93, cost = 0.048953, acc = 99.13%Epoch 94, cost = 0.045235, acc = 99.12%Epoch 95, cost = 0.045136, acc = 99.14%Epoch 96, cost = 0.048240, acc = 99.02%Epoch 97, cost = 0.049063, acc = 99.21%Epoch 98, cost = 0.045373, acc = 99.23%Epoch 99, cost = 0.046127, acc = 99.12%Epoch 100, cost = 0.046864, acc = 99.10%

可以看出最后相同的数据分类，准确率比多层感知机要高（99.10% > 98.59%）。

3、LSTMNet

LSTMNet是使用长短时记忆网络（Long Short-Term Memory, LSTM）构建的神经网络，核心思想是引入了一个名为"记忆单元"的结构，该结构可以在一定程度上保留长期依赖信息，LSTM中的每个单元包括一个输入门（input gate）、一个遗忘门（forget gate）和一个输出门（output gate），这些门的作用是控制信息在记忆单元中的流动，以便网络可以学习何时存储、更新或输出有用的信息。

import numpy as npimport torchfrom torch import optim, nnfrom data_util import load_mnistclass LSTMNet(torch.nn.Module):def __init__(self, input_dim, hidden_dim, output_dim):super(LSTMNet, self).__init__()self.hidden_dim = hidden_dimself.lstm = nn.LSTM(input_dim, hidden_dim)self.linear = nn.Linear(hidden_dim, output_dim, bias=False)def forward(self, x):batch_size = x.size()[1]h0 = torch.zeros([1, batch_size, self.hidden_dim])c0 = torch.zeros([1, batch_size, self.hidden_dim])fx, _ = self.lstm.forward(x, (h0, c0))return self.linear.forward(fx[-1])def train(model, loss, optimizer, x_val, y_val):model.train()optimizer.zero_grad()fx = model.forward(x_val)output = loss.forward(fx, y_val)output.backward()optimizer.step()return output.item()def predict(model, x_val):model.eval()output = model.forward(x_val)return output.data.numpy().argmax(axis=1)def main():torch.manual_seed(42)trX, teX, trY, teY = load_mnist(notallow=False)train_size = len(trY)n_classes = 10seq_length = 28input_dim = 28hidden_dim = 128batch_size = 100epochs = 100trX = trX.reshape(-1, seq_length, input_dim)teX = teX.reshape(-1, seq_length, input_dim)trX = np.swapaxes(trX, 0, 1)teX = np.swapaxes(teX, 0, 1)trX = torch.from_numpy(trX).float()teX = torch.from_numpy(teX).float()trY = torch.tensor(trY)model = LSTMNet(input_dim, hidden_dim, n_classes)loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)for i in range(epochs):cost = 0.num_batches = train_size // batch_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += train(model, loss, optimizer,trX[:, start:end, :], trY[start:end])predY = predict(model, teX)print("Epoch %d, cost = %f, acc = %.2f%%" %(i + 1, cost / num_batches, 100. * np.mean(predY == teY)))if __name__ == "__main__":main()

（1）以上这段代码通用的部分就不解释了，具体说LSTMNet类：

• self.lstm = nn.LSTM(input_dim, hidden_dim)创建一个LSTM层，输入维度为input_dim，隐藏层维度为hidden_dim；
• self.linear = nn.Linear(hidden_dim, output_dim, bias=False)创建一个线性层（全连接层），输入维度为hidden_dim，输出维度为output_dim，并设置不使用偏置项（bias）；
• h0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM层的隐藏状态h0，全零张量，形状为[1, batch_size, hidden_dim]；
• c0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM层的细胞状态c0，全零张量，形状为[1, batch_size, hidden_dim]；
• fx, _ = self.lstm.forward(x, (h0, c0))将输入数据x以及初始隐藏状态h0和细胞状态c0传入LSTM层，得到LSTM层的输出fx；
• return self.linear.forward(fx[-1])将LSTM层的输出传入线性层进行计算，得到最终输出。这里fx[-1]表示取LSTM层输出的最后一个时间步的数据；

（2）print("第%d轮，损失值=%f，准确率=%.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))。打印出当前训练轮次的信息，其中包括损失值和准确率，以上代码的输出结果如下：

Epoch 91, cost = 0.000468, acc = 98.57%Epoch 92, cost = 0.000452, acc = 98.57%Epoch 93, cost = 0.000437, acc = 98.58%Epoch 94, cost = 0.000422, acc = 98.57%Epoch 95, cost = 0.000409, acc = 98.58%Epoch 96, cost = 0.000396, acc = 98.58%Epoch 97, cost = 0.000384, acc = 98.57%Epoch 98, cost = 0.000372, acc = 98.56%Epoch 99, cost = 0.000360, acc = 98.55%Epoch 100, cost = 0.000349, acc = 98.55%

4、辅助代码

两篇文章的from data_util import load_mnist的data_util.py代码如下：

import gzip
import os
import urllib.request as request
from os import path
import numpy as np

DATASET_DIR = 'datasets/'
MNIST_FILES = ["train-images-idx3-ubyte.gz", "train-labels-idx1-ubyte.gz", "t10k-images-idx3-ubyte.gz", "t10k-labels-idx1-ubyte.gz"]

def download_file(url, local_path):
    dir_path = path.dirname(local_path)
    if not path.exists(dir_path):
        print("创建目录'%s' ..." % dir_path)
        os.makedirs(dir_path)
    print("从'%s'下载中 ..." % url)
    request.urlretrieve(url, local_path)

def download_mnist(local_path):
    url_root = "http://yann.lecun.com/exdb/mnist/"
    for f_name in MNIST_FILES:
        f_path = os.path.join(local_path, f_name)
        if not path.exists(f_path):
            download_file(url_root + f_name, f_path)

def one_hot(x, n):
    if type(x) == list:
        x = np.array(x)
    x = x.flatten()
    o_h = np.zeros((len(x), n))
    o_h[np.arange(len(x)), x] = 1
    return o_h

def load_mnist(ntrain=60000, ntest=10000, notallow=True):
    data_dir = os.path.join(DATASET_DIR, 'mnist/')
    if not path.exists(data_dir):
        download_mnist(data_dir)
    else:
        # 检查所有文件
        checks = [path.exists(os.path.join(data_dir, f)) for f in MNIST_FILES]
        if not np.all(checks):
            download_mnist(data_dir)
    
    with gzip.open(os.path.join(data_dir, 'train-images-idx3-ubyte.gz')) as fd:
        buf = fd.read()
        loaded = np.frombuffer(buf, dtype=np.uint8)
        trX = loaded[16:].reshape((60000, 28 * 28)).astype(float)
    
    with gzip.open(os.path.join(data_dir, 'train-labels-idx1-ubyte.gz')) as fd:
        buf = fd.read()
        loaded = np.frombuffer(buf, dtype=np.uint8)
        trY = loaded[8:].reshape((60000))
    
    with gzip.open(os.path.join(data_dir, 't10k-images-idx3-ubyte.gz')) as fd:
        buf = fd.read()
        loaded = np.frombuffer(buf, dtype=np.uint8)
        teX = loaded[16:].reshape((10000, 28 * 28)).astype(float)
    
    with gzip.open(os.path.join(data_dir, 't10k-labels-idx1-ubyte.gz')) as fd:
        buf = fd.read()
        loaded = np.frombuffer(buf, dtype=np.uint8)
        teY = loaded[8:].reshape((10000))
    
    trX /= 255.
    teX /= 255.
    trX = trX[:ntrain]
    trY = trY[:ntrain]
    teX = teX[:ntest]
    teY = teY[:ntest]
    
    if onehot:
        trY = one_hot(trY, 10)
        teY = one_hot(teY, 10)
    else:
        trY = np.asarray(trY)
        teY = np.asarray(teY)
    
    return trX, teX, trY, teY

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