python-3.x - 为什么单层 MLP 在数字分类器中优于多层？

Question

我正在使用 MLP 分类器对 MNIST 数据集进行数字分类。我观察到非常奇怪的行为。单层分类器比多层分类器更好。虽然增加单层神经元数量似乎会提高准确性。为什么多层不比单层好？这是我的代码:

param_grid={'hidden_layer_sizes':[400,300,200,100,70,50,20,10]}
grid=GridSearchCV(MLPClassifier(random_state=1),param_grid,cv=3,scoring='accuracy')
grid.fit(train_data.iloc[:,1:],train_data.iloc[:,0])
grid.grid_scores_

输出:

[mean: 0.97590, std: 0.00111, params: {'hidden_layer_sizes': 400},
 mean: 0.97300, std: 0.00300, params: {'hidden_layer_sizes': 300},
 mean: 0.97271, std: 0.00065, params: {'hidden_layer_sizes': 200},
 mean: 0.97052, std: 0.00143, params: {'hidden_layer_sizes': 100},
 mean: 0.96507, std: 0.00262, params: {'hidden_layer_sizes': 70},
 mean: 0.96448, std: 0.00150, params: {'hidden_layer_sizes': 50},
 mean: 0.94531, std: 0.00378, params: {'hidden_layer_sizes': 20},
 mean: 0.92945, std: 0.00320, params: {'hidden_layer_sizes': 10}]

对于多层:

param_grid={'hidden_layer_sizes':[[200],[200,100],[200,100,50],[200,100,50,20],[200,100,50,20,10]]}
grid=GridSearchCV(MLPClassifier(random_state=1),param_grid,cv=3,scoring='accuracy')
grid.fit(train_data.iloc[:,1:],train_data.iloc[:,0])
grid.grid_scores_

输出:

[mean: 0.97271, std: 0.00065, params: {'hidden_layer_sizes': [200]},
 mean: 0.97255, std: 0.00325, params: {'hidden_layer_sizes': [200, 100]},
 mean: 0.97043, std: 0.00199, params: {'hidden_layer_sizes': [200, 100, 50]},
 mean: 0.96755, std: 0.00173, params: {'hidden_layer_sizes': [200, 100, 50, 20]},
 mean: 0.96086, std: 0.00511, params: {'hidden_layer_sizes': [200, 100, 50, 20, 10]}]

关于数据集:28*28像素的手写数字图像。

Answer 1

在我看来，你的模型过度拟合。您可以通过比较 train_scores(使用参数 return_train_score=True)与 test_scores 来检查这一点。

如果已经过度拟合，那么让你的神经网络更深或增加隐藏层中的单元可能会让情况变得更糟。因此，请尝试获取更多数据和/或找到合适的 alpha(正则化参数)以使您的模型表现更好。