【李沐】动手学习ai思路softmax回归实现

来源：https://www.cnblogs.com/blzm742624643/p/15079086.html

一、从零开始实现

1.1 首先引入Fashion-MNIST数据集

1 import torch
2 from IPython import display
3 from d2l import torch as d2l
4 
5 batch_size = 256
6 train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

1.2 初始化模型参数

原始图像中每个样本都是28*28的，所以要展平每个图像成长度为784的向量。

权重784*10，偏置1*10

1 num_inputs = 784
2 num_outputs = 10
3 
4 W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)
5 b = torch.zeros(num_outputs, requires_grad=True)

1.3 定义softmax操作

如果为0则留下一行，为1则留下一列

X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
X.sum(0, keepdim=True), X.sum(1, keepdim=True)

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

1 X = torch.normal(0, 1, (2, 5))
2 X_prob = softmax(X)
3 X_prob, X_prob.sum(1)

1.4 模型定义

-1 的地方为批次， W.shape[0]为输入的维度

1 def net(X):
2     return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)

1.5 损失函数

通过 y 来获取 y_hat 中的值

1 y = torch.tensor([0, 2])
2 y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
3 y_hat[[0, 1], y]

学会了以上的操作我们就可以用一行来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])

cross_entropy(y_hat, y)

1.6 分类准确率

假设y_hat是一个矩阵，第二个维度存储每个类的预测分数。使用argmax获得每行中的最大元素。

def accuracy(y_hat, y):  #@save
    """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())

在评估模式的时候不计算梯度，只做前向传递

1 def evaluate_accuracy(net, data_iter):  #@save
2     """计算在指定数据集上模型的精度。"""
3     if isinstance(net, torch.nn.Module):
4         net.eval()  # 将模型设置为评估模式
5     metric = Accumulator(2)  # 正确预测数、预测总数
6     for X, y in data_iter:
7         metric.add(accuracy(net(X), y), y.numel())
8     return metric[0] / metric[1]

关于用于对多个变量进行累加的Accumulator类的实现

 1 class Accumulator:  #@save
 2     """在`n`个变量上累加。"""
 3     def __init__(self, n):
 4         self.data = [0.0] * n
 5 
 6     def add(self, *args):
 7         self.data = [a + float(b) for a, b in zip(self.data, args)]
 8 
 9     def reset(self):
10         self.data = [0.0] * len(self.data)
11 
12     def __getitem__(self, idx):
13         return self.data[idx]

由于随机权重初始化net模型，所以准确率近似于随机猜测

1 evaluate_accuracy(net, test_iter)

1.7 训练

updater 是更新模型参数的常用函数，它接受批量大小作为参数。它可以是封装的d2l.sgd函数，也可以是框架的内置优化函数。

def train_epoch_ch3(net, train_iter, loss, updater):  #@save
    """训练模型一个迭代周期（定义见第3章）。"""
    # 将模型设置为训练模式
    if isinstance(net, torch.nn.Module):
        net.train()
    # 训练损失总和、训练准确度总和、样本数
    metric = Accumulator(3)
    for X, y in train_iter:
        # 计算梯度并更新参数
        y_hat = net(X)
        l = loss(y_hat, y)
        if isinstance(updater, torch.optim.Optimizer):
            # 使用PyTorch内置的优化器和损失函数
            updater.zero_grad()
            # 计算梯度
            l.backward()  
            # 更新参数
            updater.step()
            metric.add(
                float(l) * len(y), accuracy(y_hat, y),
                y.size().numel())
        else:
            # 使用定制的优化器和损失函数
            l.sum().backward()
            updater(X.shape[0])
            metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    # 返回训练损失和训练准确率
    return metric[0] / metric[2], metric[1] / metric[2]

辅助函数

class Animator:  #@save
    """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)

进行num_epochs个迭代周期的训练，每个迭代周期结束利用test_iter访问到的测试数据集对模型进行评估。

 1 def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  #@save
 2     """训练模型（定义见第3章）。"""
 3     animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],
 4                         legend=['train loss', 'train acc', 'test acc'])
 5     for epoch in range(num_epochs):
 6         train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
 7         test_acc = evaluate_accuracy(net, test_iter)
 8         animator.add(epoch + 1, train_metrics + (test_acc,))
 9     train_loss, train_acc = train_metrics
10     assert train_loss < 0.5, train_loss
11     assert train_acc <= 1 and train_acc > 0.7, train_acc
12     assert test_acc <= 1 and test_acc > 0.7, test_acc

1 lr = 0.1
2 
3 def updater(batch_size):
4     return d2l.sgd([W, b], lr, batch_size)
5 
6 num_epochs = 10
7 train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)

1.8 预测

def predict_ch3(net, test_iter, n=6):  #@save
    """预测标签（定义见第3章）。"""
    # 拿出一个样本
    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, pred in zip(trues, preds)]
    d2l.show_images(X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])

predict_ch3(net, test_iter)