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3.12 权重衰减
本节介绍应对过拟合的常用方法
3.12.1 方法
正则化通过为模型损失函数添加惩罚项使学出的模型参数更小,是应对过拟合的常用手段。
3.12.2 高维线性回归实验 import torch
import torch.nn as nn
import numpy as np
import sys
sys.path.append(..)
import d2lzh_pytorch as d2ln_train, n_test, num_inputs 20, 100, 200
true_w, true_b torch.ones(num_inputs, 1) * 0.01, 0.05features torch.randn((n_train n_test, num_inputs))
labels torch.matmul(features, true_w) true_b
labels torch.tensor(np.random.normal(0, 0.01, sizelabels.size()), dtypetorch.float)
train_features, test_features features[:n_train, :], features[n_train:, :]
train_labels, test_labels labels[:n_train], labels[n_train:]3.13.3 从零开始实现
3.12.3.1 初始化模型参数
def init_params():w torch.randn((num_inputs, 1), requires_gradTrue)b torch.zeros(1, requires_gradTrue)return [w, b]3.12.3.2 定义L2范数惩罚项
def l2_penalty(w):return (w**2).sum() / 23.12.3.3 定义训练和测试
batch_size, num_epochs, lr 1, 100, 0.003
net, loss d2l.linreg, d2l.squared_lossdataset torch.utils.data.TensorDataset(train_features, train_labels)
train_iter torch.utils.data.DataLoader(dataset, batch_size, shuffleTrue)def fit_and_plot(lambd):w, b init_params()train_ls, test_ls [], []for _ in range(num_epochs):for X, y in train_iter:# 添加了L2范数惩罚项l loss(net(X, w, b), y) lambd * l2_penalty(w)l l.sum()if w.grad is not None:w.grad.data.zero_()b.grad.data.zero_()l.backward()d2l.sgd([w, b], lr, batch_size)train_ls.append(loss(net(train_features, w, b), train_labels).mean().item())test_ls.append(loss(net(test_features, w, b), test_labels).mean().item())d2l.semilogy(range(1, num_epochs 1), train_ls, epochs, loss,range(1, num_epochs 1), test_ls, [train, test])print(L2 norm of w:, w.norm().item())3.12.3.4 观察过拟合
fit_and_plot(lambd0)3.12.3.5 使用权重衰减
fit_and_plot(lambd5)3.12.4 简洁实现
def fit_and_plot_pytorch(wd):# 对权重参数衰减。权重名称一般以weight结尾net nn.Linear(num_inputs, 1)nn.init.normal_(net.weight, mean0, std1)nn.init.normal_(net.bias, mean0 , std1)optimizer_w torch.optim.SGD(params[net.weight], lr lr, weight_decaywd) # 对权重进行衰减optimizer_b torch.optim.SGD(params[net.bias], lrlr) # 对偏差不进行衰减train_ls, test_ls [], []for _ in range(num_epochs):for X, y in train_iter:l loss(net(X), y).mean()optimizer_w.zero_grad()optimizer_b.zero_grad()l.backward()# 对两个optimizer实例分别调用step函数,从而分别更新权重和偏差optimizer_w.step()optimizer_b.step()train_ls.append(loss(net(train_features), train_labels).mean().item())test_ls.append(loss(net(test_features), test_labels).mean().item())d2l.semilogy(range(1, num_epochs 1), train_ls, epochs, loss,range(1, num_epochs 1), test_ls, [train, test])print(L2 norm of w:, net.weight.data.norm().item())fit_and_plot_pytorch(0)fit_and_plot_pytorch(3)
