2.4.4　采用正则化避免过拟合

假设我们还想进一步提升模型的预测能力，希望通过下面更复杂的神经网络模型来实现。模型训练好后，通过plot()函数查看每一个训练周期的训练集和验证集的损失值和准确率。结果如图2-15所示。

> bigger_model <- keras_model_sequential()
> bigger_model %>%
+   layer_dense(units = 128,kernel_initializer = 'uniform',
+               activation = 'relu',input_shape = c(16)) %>%
+   layer_dense(units = 64,kernel_initializer = 'uniform',
+               activation = 'relu') %>%
+   layer_dense(units = 32,kernel_initializer = 'uniform',
+               activation = 'relu') %>%
+   layer_dense(units = 16,kernel_initializer = 'uniform',
+               activation = 'relu') %>%
+   layer_dense(units = 8,kernel_initializer = 'uniform',
+               activation = 'relu') %>%
+   layer_dense(units = 4,kernel_initializer = 'uniform',
+               activation = 'relu') %>%
+   layer_dense(units = 1,kernel_initializer = 'uniform',
+               activation = 'sigmoid')
> bigger_model %>% compile(loss='binary_crossentropy',
+                   optimizer='rmsprop',
+                   metrics=c('accuracy'))
> history <- bigger_model %>% fit(
+   x_train_scale, y_train,
+   batch_size = 128,
+   epochs = 150,
+   verbose = 1,
+   validation_split = 0.2
+ )
> plot(history)

图2-15　训练和验证的损失及准确率

从图2-15可知，随着训练周期增加，训练集的损失不断减少，准确率不断提升；但是验证集在训练周期大于60后，损失不断增加，准确率也有所下降。出现明显过拟合现象。

我们利用L2正则化重新训练一个模型，并对比两者差异。结果如图2-16所示。

> # 增加L2正则化
> l2_model <- keras_model_sequential()
> l2_model %>%
+   layer_dense(units = 128,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu',input_shape = c(16)) %>%
+   layer_dense(units = 64,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu') %>%
+   layer_dense(units = 32,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu') %>%
+   layer_dense(units = 16,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu') %>%
+   layer_dense(units = 8,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu') %>%
+   layer_dense(units = 4,kernel_initializer = 'uniform',
+               kernel_regularizer = regularizer_l2(l = 0.001),
+               activation = 'relu') %>%
+   layer_dense(units = 1,kernel_initializer = 'uniform',
+               activation = 'sigmoid')
>
> l2_model %>% compile(loss='binary_crossentropy',
+                      optimizer='rmsprop',
+                      metrics=c('accuracy'))
> l2_history <- l2_model %>% fit(
+  x_train_scale, y_train,
+  batch_size = 128,
+  epochs = 150,
+  verbose = 0,
+  validation_split = 0.2
+)
> # 对比两个模型效果
> library(ggplot2)
> library(tidyr)
> library(dplyr)
> library(tibble)
> compare_cx <- data.frame(
+   baseline_train = history$metrics$loss,
+   baseline_val = history$metrics$val_loss,
+   l2_train = l2_history$metrics$loss,
+   l2_val = l2_history$metrics$val_loss
+ ) %>%
+   rownames_to_column() %>%
+   mutate(rowname = as.integer(rowname)) %>%
+   gather(key = "type", value = "value", -rowname)
> ggplot(compare_cx, aes(x = rowname, y = value, color = type)) +
+   geom_line() +
+   xlab("epoch") +
+   ylab("loss") +
+   theme_bw()+
+   theme(
+     legend.position="none",
+     plot.title=element_text(colour="gray24",size=12,face="bold"),
+     plot.background = element_rect(fill = "gray90"),
+     axis.title=element_text(size=10),
+     axis.text=element_text(colour="gray35"))

图2-16　正则化前后效果对比

图2-16中靠下的两条线分别是增加L2正则化后的训练集和验证集的损失曲线。在训练周期后期两条曲线的差异明显小于上面两条曲线。