PyTorch实现L1，L2正则化以及Dropout

1. 了解知道Dropout原理

2. 用代码实现正则化(L1、L2、Dropout）

3. Dropout的numpy实现

4. PyTorch中实现dropout

   dropout是指在深度学习网络的训练过程中，对于神经网络单元，
   按照一定的概率将其暂时从网络中丢弃。（注意是暂时）
   

   对一层神经网络的实施dropout代码实现

d = np.random.rand(3, 2) < keep_drop
a = np.multiply(a, d)
a /= keep_drop
 //对**值进行缩放，为了不影响下一层网络的最后的预期输出值，加上这个步骤来修正损失的值

1.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

2.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的numpy实现

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()