高维线性回归实验,证明权重衰减(L2范数正则化)对过拟合的减轻效果
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高维线性回归实验,证明权重衰减(L2范数正则化)对过拟合的减轻效果
n_train, n_test, num_inputs = 20, 100, 200
true_w, true_b = torch.ones(num_inputs, 1) * 0.01, 0.05
#生成数据
features = 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, size=labels.size()), dtype=torch.float)
train_features, test_features = features[:n_train, :], features[n_train:, :] #20\\100
train_labels, test_labels = labels[:n_train], labels[n_train:]
def init_params():
w = torch.randn((num_inputs, 1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)
return [w, b]
def l2_penalty(w): # L2范数惩罚项
return (w**2).sum() / 2
batch_size, num_epochs, lr = 1, 100, 0.003
def linreg(X, w, b): # 本函数已保存在d2lzh_pytorch包中方便以后使用
return torch.mm(X, w) + b
def squared_loss(y_hat, y): # 本函数已保存在d2lzh_pytorch包中⽅便以后使⽤
# 注意这⾥返回的是向量, 另外, pytorch⾥的MSELoss并没有除以 2
return (y_hat - y.view(y_hat.size())) ** 2 / 2
net, loss = linreg, squared_loss
dataset = torch.utils.data.TensorDataset(train_features, train_labels)
train_iter = torch.utils.data.DataLoader(dataset, batch_size, shuffle=True)
def sgd(params, lr, batch_size): # 本函数已保存在d2lzh_pytorch包中⽅便以后使⽤
for param in params:
param.data -= lr * param.grad / batch_size # 注意这⾥更改param时⽤的param.data
def set_figsize(figsize=(3.5, 2.5)):
use_svg_display()
# 设置图的尺寸
plt.rcParams['figure.figsize'] = figsize
def use_svg_display():
"""Use svg format to display plot in jupyter"""
display.set_matplotlib_formats('svg')
def semilogy(x_vals, y_vals, x_label, y_label, x2_vals=None, y2_vals=None,
legend=None, figsize=(3.5, 2.5)):
set_figsize(figsize)
plt.xlabel(x_label)
plt.ylabel(y_label)
plt.semilogy(x_vals, y_vals)
if x2_vals and y2_vals:
plt.semilogy(x2_vals, y2_vals, linestyle=':')
plt.legend(legend)
num_epochs, loss = 100, torch.nn.MSELoss()
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()
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())
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())
import torch.nn as nn
#用potorch实现正则化
def fit_and_plot_pytorch(wd):
# 对权重参数衰减。权重名称一般是以weight结尾
net = nn.Linear(num_inputs, 1)
nn.init.normal_(net.weight, mean=0, std=1)
nn.init.normal_(net.bias, mean=0, std=1)
optimizer_w = torch.optim.SGD(params=[net.weight], lr=lr, weight_decay=wd) # 对权重参数衰减
optimizer_b = torch.optim.SGD(params=[net.bias], lr=lr) # 不对偏差参数衰减
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())
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(lambd=0) #不加正则化,
fit_and_plot(lambd=3) #加正则化
fit_and_plot_pytorch(0)
fit_and_plot_pytorch(3)
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