過擬合是當數據量較小時或者輸出結果過于依賴某些特定的神經元,訓練神經網絡訓練會發生一種現象。出現這種現象的神經網絡預測的結果并不具有普遍意義,其預測結果極不準確。
import torch
import matplotlib.pyplot as plt
N_SAMPLES = 20
N_HIDDEN = 300
# train數據
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))
# test數據
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))
# 可視化
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()
# 網絡一,未使用dropout正規化
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),
)
# 網絡二,使用dropout正規化
net_dropped = torch.nn.Sequential(
torch.nn.Linear(1, N_HIDDEN),
torch.nn.Dropout(0.5), # 隨機屏蔽50%的網絡連接
torch.nn.ReLU(),
torch.nn.Linear(N_HIDDEN, N_HIDDEN),
torch.nn.Dropout(0.5), # 隨機屏蔽50%的網絡連接
torch.nn.ReLU(),
torch.nn.Linear(N_HIDDEN, 1),
)
# 選擇優化器
optimizer_ofit = torch.optim.Adam(net_overfitting.parameters(), lr=0.01)
optimizer_drop = torch.optim.Adam(net_dropped.parameters(), lr=0.01)
# 選擇計算誤差的工具
loss_func = torch.nn.MSELoss()
plt.ion()
for t in range(500):
# 神經網絡訓練數據的固定過程
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:
# 脫離訓練模式,這里便于展示神經網絡的變化過程
net_overfitting.eval()
net_dropped.eval()
# 可視化
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.numpy(),
fontdict={'size': 20, 'color': 'red'})
plt.text(0, -1.5, 'dropout loss=%.4f' % loss_func(test_pred_drop, test_y).data.numpy(),
fontdict={'size': 20, 'color': 'blue'})
plt.legend(loc='upper left'); plt.ylim((-2.5, 2.5));plt.pause(0.1)
# 重新進入訓練模式,并繼續上次訓練
net_overfitting.train()
net_dropped.train()
plt.ioff()
plt.show()