【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