李沐《动手学深度学习》课程笔记：09 Softmax回归

目录

09 Softmax回归

1.Softmax回归

2.损失函数

​​​​​​3.图片分类数据集

4. Softmax回归的从零开始实现

​5.Softmax回归的简洁实现

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09 Softmax回归

1.Softmax回归

2.损失函数

3.图片分类数据集

# MNIST数据集是图像分类中广泛使用的数据集之一，但作为基准数据集过于简单。我们将使用类似但复杂的Fashion-MNIST数据集
import torch
import torchvision
from torch.utils import data
from torchvision import transforms
from d2l import torch as d2l
import os
import matplotlib.pyplot as plt
os.environ["KMP_DUPLICATE_LIB_OK"] = "TRUE"

d2l.use_svg_display()

# 通过框架中的内置函数将Fashion-MINIST数据集下载并读取到内存中
# 通过ToTensor实例将图像数据从PIL类型变换成32位浮点数格式
# 并除以255使得所有像素的数值均在0到1之间

trans = transforms.ToTensor()
mnist_train = torchvision.datasets.FashionMNIST(root=r'C:\Users\mm\Desktop\FashionMNIST', train=True,
                                                transform=trans, download=True)
mnist_test = torchvision.datasets.FashionMNIST(root=r'C:\Users\mm\Desktop\FashionMNIST', train=False,
                                               transform=trans, download=True)

print(len(mnist_train))
print(len(mnist_test))

print(mnist_train[0][0].shape)


# 两个可视化数据集的函数
def get_fashion_mnist_labels(labels):
    '''返回Fashion-MNIST数据集的文本标签'''
    text_labels = [
        't-shirt', 'trouser', 'pullover', 'dress', 'coat', 'sandal', 'shirt','sneaker', 'bag', 'ankle boot'
    ]
    return [text_labels[int(i)] for i in labels]


def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):
    '''Plot a list of images.'''
    figsize = (num_cols * scale, num_rows * scale)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        if torch.is_tensor(img):
            # 图片张量
            ax.imshow(img.numpy())

        else:
            # PIL图片
            ax.imshow(img)

        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])

    plt.show()
    return axes


# 几个样本的图像及其相应的标签
X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))
show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y))


# 读取一小批量数据，大小为batch_size
batch_size = 256


def get_dataloader_workers():
    '''使用4个进程来读取的数据'''
    return 4


train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True, num_workers=get_dataloader_workers())
timer = d2l.Timer()
for X, y in train_iter:
    continue

print(f'{timer.stop():.2f} sec')


# 定义load_data_fashion_mnist函数
def load_data_fashion_mnist(batch_size, resize=None):
    '''下载Fashion-MNIST数据集，然后将其加载到内存中'''
    trans = [transforms.ToTensor()]
    if resize:
        trans.insert(0, transforms.Resize(resize))
    trans = transforms.Compose(trans)
    mnist_train = torchvision.datasets.FashionMNIST(root=r'C:\Users\mm\Desktop\FashionMNIST', train=True, transform=trans, download=True)
    mnist_test = torchvision.datasets.FashionMNIST(root=r'C:\Users\mm\Desktop\FashionMNIST', train=False, transform=trans, download=True)
    return (data.DataLoader(mnist_train, batch_size, shuffle=True, num_workers=get_dataloader_workers()),
            data.DataLoader(mnist_train, batch_size, shuffle=False, num_workers=get_dataloader_workers()))


train_iter, test_iter = load_data_fashion_mnist(32, resize=64)
for X, y in train_iter:
    print(X.shape, X.dtype, y.shape, y.dtype)
    break

60000
10000
torch.Size([1, 28, 28])

 ​

4.76 sec

torch.Size([32, 1, 64, 64]) torch.float32 torch.Size([32]) torch.int64

4. Softmax回归的从零开始实现

import torch
from IPython import display
from d2l import torch as d2l
import matplotlib.pyplot as plt
import os
os.environ["KMP_DUPLICATE_LIB_OK"] = "TRUE"

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

# 将展平每个图像，将它们视为长度为784的向量。因为我们的数据集有10个类别，所以网络输出维度为10
num_inputs = 784
num_outputs = 10

W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)
b = torch.zeros(num_outputs, requires_grad=True)

# 给定一个矩阵X，我们可以对所有元素求和
X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
print(X.sum(0, keepdim=True))
print(X.sum(1, keepdim=True))


def softmax(X):
    X_exp = torch.exp(X)
    partition = X_exp.sum(1, keepdim=True)
    return X_exp / partition  # 这里应用了广播机制


# 我们将每个元素变成一个非负数，此外，依据概率原理，每行总和为1
X = torch.normal(0, 1, (2, 5))
X_prob = softmax(X)
print(X_prob)
print(X_prob.sum(1))


# 实现Softmax回归模型
def net(X):
    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)


# 创建一个数据y_hat，其中包含2个样本和3个类别的预测概率，使用y作为y_hat中概率的索引
y = torch.tensor([0, 2])
y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
print(y_hat[[0, 1], y])


# 实现交叉熵损失函数
def cross_entropy(y_hat, y):
    return -torch.log(y_hat[range(len(y_hat)), y])


print(cross_entropy(y_hat, y))


# 将预测类别与真实y元素进行比较
def accuracy(y_hat, y):
    '''计算预测正确的数量'''
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
        y_hat = y_hat.argmax(axis=1)
    cmp = y_hat.type(y.dtype) == y
    return float(cmp.type(y.dtype).sum())


accuracy(y_hat, y) / len(y)


# Accumulator实例中创建了2个变量，用于分别存储正确预测的数量和预测的总数量
class Accumulator:
    '''在n个变量上累加'''
    def __init__(self, n):
        self.data = [0.0] * n

    def add(self, *args):
        self.data = [a + float(b) for a, b in zip(self.data, args)]

    def reset(self):
        self.data = [0.0] * len(self.data)

    def __getitem__(self, idx):
        return self.data[idx]


# 我们可以评估在任意模型net的准确率
def evaluate_accuracy(net, data_iter):
    '''计算在指定数据集上模型的精度'''
    if isinstance(net, torch.nn.Module):
        net.eval()  # 将模型设置为评估模式
    metric = Accumulator(2)  # 正确预测数、预测总数
    for X, y in data_iter:
        metric.add(accuracy(net(X), y), y.numel())
    return metric[0] / metric[1]


# Softmax回归的训练
def train_epoch_ch3(net, train_iter, loss, updater):
    if isinstance(net, torch.nn.Module):
        net.train()
    metric = Accumulator(3)
    for X, y in train_iter:
        y_hat = net(X)
        l = loss(y_hat, y)
        if isinstance(updater, torch.optim.Optimizer):
            updater.zero_grad()
            l.backward()
            updater.step()
            metric.add(
                float(l) * len(y), accuracy(y_hat, y), y.size().numel())
        else:
            l.sum().backward()
            updater(X.shape[0])
            metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    return metric[0] / metric[2], metric[1] / metric[2]


# 定义一个在动画中绘制数据的实用程序类
class Animator:
    # 在动画中绘制数据
    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None, ylim=None, xscale='linear', yscale='linear', fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1, figsize=(3.5, 2.5)):
        # 增量地绘制多条线
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes,]
        # 使用lambda函数捕获参数
        self.config_axes = lambda: d2l.set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # 向图表中添加多个数据点
        if not hasattr(y, '__len__'):
            y = [y]
        n = len(y)
        if not hasattr(x, '__len__'):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] for _ in range(n)]
        for i, (a, b) in enumerate(zip(x, y)):
            if a is not None and b is not None:
                self.X[i].append(a)
                self.Y[i].append(b)
        self.axes[0].cla()
        for x, y, fmt in zip(self.X, self.Y, self.fmts):
            self.axes[0].plot(x, y, fmt)
        self.config_axes()
        display.display(self.fig)
        display.clear_output(wait=True)


# 训练函数
def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):
    '''训练模型'''
    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9], legend=['train loss', 'train acc', 'test acc'])
    for epoch in range(num_epochs):
        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
        test_acc = evaluate_accuracy(net, test_iter)
        animator.add(epoch + 1, train_metrics + (test_acc,))
    train_loss, train_acc = train_metrics
    assert train_loss < 0.5, train_loss
    assert 1 >= train_acc > 0.7, train_acc
    assert 1 >= test_acc > 0.7, test_acc
    plt.show()


lr = 0.1


def updater(batch_size):
    return d2l.sgd([W, b], lr, batch_size)


# 训练模型10个迭代周期
num_epochs = 10
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)


# 对图像进行分类预测
def predict_ch3(net, test_iter, n=6):
    '''预测标签'''
    for X, y in test_iter:
        break
    trues = d2l.get_fashion_mnist_labels(y)
    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))
    titles = [true + '\n' + pred for true, p    red in zip(trues, preds)]
    d2l.show_images(
        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n]
    )
    plt.show()


predict_ch3(net, test_iter)

tensor([[5., 7., 9.]])

tensor([[ 6.],
        [15.]])

tensor([[0.1659, 0.3020, 0.2751, 0.0552, 0.2018],
        [0.1170, 0.1502, 0.0258, 0.5928, 0.1143]])

tensor([1.0000, 1.0000])
tensor([0.1000, 0.5000])
tensor([2.3026, 0.6931])

5.Softmax回归的简洁实现

# 通过深度学习框架的高级API能够使实现softmax回归变得更加容易
import torch
from torch import nn
from d2l import torch as d2l
import os
import matplotlib.pyplot as plt
os.environ["KMP_DUPLICATE_LIB_OK"] = "TRUE"

batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

# Softmax回归的输出层是一个全连接层
# PyTorch不会隐式地调整输入的形状
# 因此，我们定义了展平层（flatten）在线性层前调整网络输入的形状
net = nn.Sequential(nn.Flatten(), nn.Linear(784, 10))


def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.normal_(m.weight, std=0.01)


net.apply(init_weights)

# 在交叉熵损失函数中传递未归一化的预测，并同时计算softmax及其对数
loss = nn.CrossEntropyLoss()

# 使用学习率为0.1的小批量随机梯度下降作为优化算法
trainer = torch.optim.SGD(net.parameters(), lr=0.1)

# 调用之前定义的训练函数来训练模型
num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)
plt.show()