过拟合问题——权重衰减和丢弃法

def fit_and_plot_gluon(wd):
    net = nn.Sequential()
    net.add(nn.Dense(1))
    net.initialize(init.Normal(sigma=1))
    # 对权重参数衰减。权重名称一般是以weight结尾
    trainer_w = gluon.Trainer(net.collect_params('.*weight'), 'sgd',
                              {'learning_rate': lr, 'wd': wd})
    # 不对偏差参数衰减。偏差名称一般是以bias结尾
    trainer_b = gluon.Trainer(net.collect_params('.*bias'), 'sgd',
                              {'learning_rate': lr})
    train_ls, test_ls = [], []
    for _ in range(num_epochs):
        for X, y in train_iter:
            with autograd.record():
                l = loss(net(X), y)
            l.backward()
            # 对两个Trainer实例分别调用step函数，从而分别更新权重和偏差
            trainer_w.step(batch_size)
            trainer_b.step(batch_size)
        train_ls.append(loss(net(train_features),
                             train_labels).mean().asscalar())
        test_ls.append(loss(net(test_features),
                            test_labels).mean().asscalar())
    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[0].weight.data().norm().asscalar())

import d2lzh as d2l
from mxnet import autograd, gluon, init, nd
from mxnet.gluon import loss as gloss, nn

def dropout(X, drop_prob):
    assert 0 <= drop_prob <= 1
    keep_prob = 1 - drop_prob
    # 这种情况下把全部元素都丢弃
    if keep_prob == 0:
        return X.zeros_like()
    mask = nd.random.uniform(0, 1, X.shape) < keep_prob
    return mask * X / keep_prob

num_inputs, num_outputs, num_hiddens1, num_hiddens2 = 784, 10, 256, 256

W1 = nd.random.normal(scale=0.01, shape=(num_inputs, num_hiddens1))
b1 = nd.zeros(num_hiddens1)
W2 = nd.random.normal(scale=0.01, shape=(num_hiddens1, num_hiddens2))
b2 = nd.zeros(num_hiddens2)
W3 = nd.random.normal(scale=0.01, shape=(num_hiddens2, num_outputs))
b3 = nd.zeros(num_outputs)

params = [W1, b1, W2, b2, W3, b3]
for param in params:
    param.attach_grad()
    
drop_prob1, drop_prob2 = 0.2, 0.5

def net(X):
    X = X.reshape((-1, num_inputs))
    H1 = (nd.dot(X, W1) + b1).relu()
    if autograd.is_training():  # 只在训练模型时使用丢弃法
        H1 = dropout(H1, drop_prob1)  # 在第一层全连接后添加丢弃层
    H2 = (nd.dot(H1, W2) + b2).relu()
    if autograd.is_training():
        H2 = dropout(H2, drop_prob2)  # 在第二层全连接后添加丢弃层
    return nd.dot(H2, W3) + b3

num_epochs, lr, batch_size = 5, 0.5, 256
loss = gloss.SoftmaxCrossEntropyLoss()
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, params, lr)

net = nn.Sequential()
net.add(nn.Dense(256, activation="relu"),
        nn.Dropout(drop_prob1),  # 在第一个全连接层后添加丢弃层
        nn.Dense(256, activation="relu"),
        nn.Dropout(drop_prob2),  # 在第二个全连接层后添加丢弃层
        nn.Dense(10))
net.initialize(init.Normal(sigma=0.01))
trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': lr})
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, trainer)