20正则化之Dropout

一、Dropout概念

1.1 Dropout随机失活

随机: dropout probability
失活: weight=0

基本思想：以一定的概率使网络中的部分神经元失去活性，让神经元学习到更鲁棒的特征，减轻过度的依赖性，从而缓解了过拟合，降低方差达到正则化效果

数据尺度变化: 测试时,所有权重乘以1-drop_prob
drop_prob = 0.3, 1-drop_prob = 0.7

1.2 nn.Dropout

torch.nn.Dropout(p=0.5, inplace=False)

功能: Dropout层

参数:

• p:被舍弃概率,失活概率

实现细节:
训练时权重均乘以 $\frac{1}{1-p}$，即除以1-p，而测试是乘以1-p，这样以保持尺度相同

位置：放置于要失活的网络层之前，输出层之前一般不加dropout

示例：

# -*- coding:utf-8 -*-

import torch
import torch.nn as nn
import matplotlib.pyplot as plt
from tools.common_tools import set_seed
from torch.utils.tensorboard import SummaryWriter

set_seed(1)  # 设置随机种子
n_hidden = 200
max_iter = 2000
disp_interval = 400
lr_init = 0.01


# ============================ step 1/5 数据 ============================
def gen_data(num_data=10, x_range=(-1, 1)):

    w = 1.5
    train_x = torch.linspace(*x_range, num_data).unsqueeze_(1)
    train_y = w*train_x + torch.normal(0, 0.5, size=train_x.size())
    test_x = torch.linspace(*x_range, num_data).unsqueeze_(1)
    test_y = w*test_x + torch.normal(0, 0.3, size=test_x.size())

    return train_x, train_y, test_x, test_y


train_x, train_y, test_x, test_y = gen_data(x_range=(-1, 1))


# ============================ step 2/5 模型 ============================
class MLP(nn.Module):
    def __init__(self, neural_num, d_prob=0.5):
        super(MLP, self).__init__()
        self.linears = nn.Sequential(

            nn.Linear(1, neural_num),
            nn.ReLU(inplace=True),

            nn.Dropout(d_prob),
            nn.Linear(neural_num, neural_num),
            nn.ReLU(inplace=True),

            nn.Dropout(d_prob),
            nn.Linear(neural_num, neural_num),
            nn.ReLU(inplace=True),

            nn.Dropout(d_prob),
            nn.Linear(neural_num, 1),
        )

    def forward(self, x):
        return self.linears(x)


net_prob_0 = MLP(neural_num=n_hidden, d_prob=0.)
net_prob_05 = MLP(neural_num=n_hidden, d_prob=0.5)

# ============================ step 3/5 优化器 ============================
optim_normal = torch.optim.SGD(net_prob_0.parameters(), lr=lr_init, momentum=0.9)
optim_reglar = torch.optim.SGD(net_prob_05.parameters(), lr=lr_init, momentum=0.9)

# ============================ step 4/5 损失函数 ============================
loss_func = torch.nn.MSELoss()

# ============================ step 5/5 迭代训练 ============================

writer = SummaryWriter(comment='_test_tensorboard', filename_suffix="12345678")
for epoch in range(max_iter):

    pred_normal, pred_wdecay = net_prob_0(train_x), net_prob_05(train_x)
    loss_normal, loss_wdecay = loss_func(pred_normal, train_y), loss_func(pred_wdecay, train_y)

    optim_normal.zero_grad()
    optim_reglar.zero_grad()

    loss_normal.backward()
    loss_wdecay.backward()

    optim_normal.step()
    optim_reglar.step()

    if (epoch+1) % disp_interval == 0:

        net_prob_0.eval()
        net_prob_05.eval()

        # 可视化
        for name, layer in net_prob_0.named_parameters():
            writer.add_histogram(name + '_grad_normal', layer.grad, epoch)
            writer.add_histogram(name + '_data_normal', layer, epoch)

        for name, layer in net_prob_05.named_parameters():
            writer.add_histogram(name + '_grad_regularization', layer.grad, epoch)
            writer.add_histogram(name + '_data_regularization', layer, epoch)

        test_pred_prob_0, test_pred_prob_05 = net_prob_0(test_x), net_prob_05(test_x)

        # 绘图
        plt.scatter(train_x.data.numpy(), train_y.data.numpy(), c='blue', s=50, alpha=0.3, label='train')
        plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='red', s=50, alpha=0.3, label='test')
        plt.plot(test_x.data.numpy(), test_pred_prob_0.data.numpy(), 'r-', lw=3, label='d_prob_0')
        plt.plot(test_x.data.numpy(), test_pred_prob_05.data.numpy(), 'b--', lw=3, label='d_prob_05')
        plt.text(-0.25, -1.5, 'd_prob_0 loss={:.8f}'.format(loss_normal.item()), fontdict={'size': 15, 'color': 'red'})
        plt.text(-0.25, -2, 'd_prob_05 loss={:.6f}'.format(loss_wdecay.item()), fontdict={'size': 15, 'color': 'red'})

        plt.ylim((-2.5, 2.5))
        plt.legend(loc='upper left')
        plt.title("Epoch: {}".format(epoch+1))
        plt.show()
        plt.close()

        net_prob_0.train()
        net_prob_05.train()