softmax回归从零实现

1. 加载 Fashion-MNIST 数据集

import torch
from IPython import display
from d2l import torch as d2lbatch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)

2.展平每个图像，视为长度为784的向量，数据集有10个类别，所以网络输出维度为10

num_inputs = 784
num_outputs = 10W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)
b = torch.zeros(num_outputs, requires_grad=True)

3.给定矩阵X，可以对所有元素求和

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)

4.实现softmax

def softmax(X):X_exp = torch.exp(X)partition = X_exp.sum(1, keepdim=True)return X_exp / partition

5.将每个元素变成一个非负数，依据概率原理，每行总和为1

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

6.实现softmax回归模型

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

7.创建数据y_hat，其中包含2个样本在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]])
y_hat[[0, 1], y]

8.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)

9.将预测类别与真实元素进行比较

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) == yreturn float(cmp.type(y.dtype).sum())accuracy(y_hat, y) / len(y)

10.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with torch.no_grad():for X, y in data_iter:metric.add(accuracy(net(X), y), y.numel())return metric[0] / metric[1]

11.Accumulator实例创建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] * ndef 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]evaluate_accuracy(net, test_iter)

12.softmax回归训练

def train_epoch_ch3(net, train_iter, loss, updater):"""训练模型一个迭代周期"""# 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()l.mean().backward()updater.step()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精度return metric[0] / metric[2], metric[1] / metric[2]

13.定义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, fmtsdef 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] * nif 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)

14.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

15.小批量梯度下降来优化模型的损失函数

lr = 0.1def updater(batch_size):return d2l.sgd([W, b], lr, batch_size)

16.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)

17.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:breaktrues = 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)