【Task5(2天)】PyTorch实现L1，L2正则化以及Dropout

• 了解知道Dropout原理
• 用代码实现正则化(L1、L2、Dropout）
• Dropout的numpy实现
• PyTorch中实现dropout

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了解知道Dropout原理

Dropout是防止过拟合的一种方法（过拟合overfitting指：模型在训练数据上损失函数较小，预测准确率较高；但是在测试数据上损失函数比较大，预测准确率较低。） 训练神经网络模型时，如果训练样本较少，为了防止模型过拟合，Dropout可以作为一种优化方法。

Dropout是指在神经网络的每次训练中以一个参数p为概率，使部分隐层部分神经元失活，以此来解决过拟合问题，效果可以当作用多个不同的神经网络模型在同一训练集上进行训练，最后集成求平均。Dropout还可以消除某些神经元之间的联系，增强模型的鲁棒性。

用代码实现正则化(L1、L2、Dropout）

• L1范数

  L1范数是参数矩阵W中元素的绝对值之和，L1范数相对于L0范数不同点在于，L0范数求解是NP问题，而L1范数是L0范数的最优凸近似，求解较为容易。L1常被称为LASSO.

  regularization_loss = 0
  for param in model.parameters():
      regularization_loss += torch.sum(abs(param))
  
  for epoch in range(EPOCHS):
      y_pred = model(x_train)
      classify_loss = criterion(y_pred, y_train.float().view(-1, 1))
      loss = classify_loss + 0.001 * regularization_loss  # 引入L1正则化项
  

• L2范数

  L2范数是参数矩阵W中元素的平方之和，这使得参数矩阵中的元素更稀疏，与前两个范数不同的是，它不会让参数变为0，而是使得参数大部分都接近于0。L1追求稀疏化，从而丢弃了一部分特征（参数为0），而L2范数只是使参数尽可能为0，保留了特征。L2被称为Rigde.

  optimizer = torch.optim.SGD(model.parameters(), lr=1e-1, momentum=0.9, weight_decay=0.001)
  

• Dropout

  import numpy as np
  
  X = np.array([ [0,0,1],[0,1,1],[1,0,1],[1,1,1] ])
  
  y = np.array([[0,1,1,0]]).T
  
  alpha,hidden_dim,dropout_percent,do_dropout = (0.5,4,0.2,True)
  
  synapse_0 = 2*np.random.random((3,hidden_dim)) - 1
  
  synapse_1 = 2*np.random.random((hidden_dim,1)) - 1
  
  for j in xrange(60000):
  
      layer_1 = (1/(1+np.exp(-(np.dot(X,synapse_0)))))
  
      if(do_dropout):
  
          layer_1 *= np.random.binomial([np.ones((len(X),hidden_dim))],1-dropout_percent)[0] * (1.0/(1-dropout_percent))
  
      layer_2 = 1/(1+np.exp(-(np.dot(layer_1,synapse_1))))
  
      layer_2_delta = (layer_2 - y)*(layer_2*(1-layer_2))
  
      layer_1_delta = layer_2_delta.dot(synapse_1.T) * (layer_1 * (1-layer_1))
  
      synapse_1 -= (alpha * layer_1.T.dot(layer_2_delta))
  
      synapse_0 -= (alpha * X.T.dot(layer_1_delta))
  

PyTorch中实现Dropout

import torch
from torch.autograd import Variable
import matplotlib.pyplot as plt

# torch.manual_seed(1)    # reproducible

N_SAMPLES = 20
N_HIDDEN = 300

# training data
x = torch.unsqueeze(torch.linspace(-1, 1, N_SAMPLES), 1)
y = x + 0.3*torch.normal(torch.zeros(N_SAMPLES, 1), torch.ones(N_SAMPLES, 1))
x, y = Variable(x), Variable(y)

# test data
test_x = torch.unsqueeze(torch.linspace(-1, 1, N_SAMPLES), 1)
test_y = test_x + 0.3*torch.normal(torch.zeros(N_SAMPLES, 1), torch.ones(N_SAMPLES, 1))
test_x, test_y = Variable(test_x, volatile=True), Variable(test_y, volatile=True)

# show data
'''
plt.scatter(x.data.numpy(), y.data.numpy(), c='magenta', s=50, alpha=0.5, label='train')
plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='cyan', s=50, alpha=0.5, label='test')
plt.legend(loc='upper left')
plt.ylim((-2.5, 2.5))
plt.show()
'''

net_overfitting = torch.nn.Sequential(
    torch.nn.Linear(1, N_HIDDEN),
    torch.nn.ReLU(),
    torch.nn.Linear(N_HIDDEN, N_HIDDEN),
    torch.nn.ReLU(),
    torch.nn.Linear(N_HIDDEN, 1),
)

net_dropped = torch.nn.Sequential(
    torch.nn.Linear(1, N_HIDDEN),
    torch.nn.Dropout(0.5),  # drop 50% of the neuron
    torch.nn.ReLU(),
    torch.nn.Linear(N_HIDDEN, N_HIDDEN),
    torch.nn.Dropout(0.5),  # drop 50% of the neuron
    torch.nn.ReLU(),
    torch.nn.Linear(N_HIDDEN, 1),
)

print(net_overfitting)  # net architecture
print(net_dropped)

optimizer_ofit = torch.optim.Adam(net_overfitting.parameters(), lr=0.01)
optimizer_drop = torch.optim.Adam(net_dropped.parameters(), lr=0.01)
loss_func = torch.nn.MSELoss()

plt.ion()   # something about plotting

for t in range(500):
    pred_ofit = net_overfitting(x)
    pred_drop = net_dropped(x)

    loss_ofit = loss_func(pred_ofit, y)
    loss_drop = loss_func(pred_drop, y)

    optimizer_ofit.zero_grad()
    optimizer_drop.zero_grad()
    loss_ofit.backward()
    loss_drop.backward()
    optimizer_ofit.step()
    optimizer_drop.step()

    if t % 10 == 0:
        # change to eval mode in order to fix drop out effect
        net_overfitting.eval()
        net_dropped.eval()  # parameters for dropout differ from train mode

        # plotting
        plt.cla()
        test_pred_ofit = net_overfitting(test_x)
        test_pred_drop = net_dropped(test_x)
        plt.scatter(x.data.numpy(), y.data.numpy(), c='magenta', s=50, alpha=0.3, label='train')
        plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='cyan', s=50, alpha=0.3, label='test')
        plt.plot(test_x.data.numpy(), test_pred_ofit.data.numpy(), 'r-', lw=3, label='overfitting')
        plt.plot(test_x.data.numpy(), test_pred_drop.data.numpy(), 'b--', lw=3, label='dropout(50%)')
        plt.text(0, -1.2, 'overfitting loss=%.4f' % loss_func(test_pred_ofit, test_y).data[0], fontdict={'size': 20, 'color':  'red'})
        plt.text(0, -1.5, 'dropout loss=%.4f' % loss_func(test_pred_drop, test_y).data[0], fontdict={'size': 20, 'color': 'blue'})
        plt.legend(loc='upper left'); plt.ylim((-2.5, 2.5));plt.pause(0.1)

        # change back to train mode
        net_overfitting.train()
        net_dropped.train()

plt.ioff()
plt.show()

参考：

最优化方法：L1和L2正则化regularization

PyTorch实现L1，L2正则化以及Dropout

pytorch 加正则化的方法