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使用scikit-learn为PyTorch模型进行超参数网格搜索

团购专家 • • 人工智能

使用scikit-learn为PyTorch模型进行超参数网格搜索

scikit-learn是Python中最好的机器学习库，而PyTorch又为我们构建模型提供了方便的操作，能否将它们的优点整合起来呢？在本文中，我们将介绍如何使用 scikit-learn中的网格搜索功能来调整 PyTorch 深度学习模型的超参数:

  • 如何包装 PyTorch 模型以用于 scikit-learn 以及如何使用网格搜索
  • 如何网格搜索常见的神经网络参数，如学习率、Dropout、epochs、神经元数
  • 在自己的项目上定义自己的超参数调优实验

如何在 scikit-learn 中使用 PyTorch 模型

要让PyTorch 模型可以在 scikit-learn 中使用的一个最简单的方法是使用skorch包。这个包为 PyTorch 模型提供与 scikit-learn 兼容的 API。 在skorch中，有分类神经网络的NeuralNetClassifier和回归神经网络的NeuralNetRegressor。

pip install skorch

要使用这些包装器，必须使用 nn.Module 将 PyTorch 模型定义为类，然后在构造 NeuralNetClassifier 类时将类的名称传递给模块参数。 例如：

class MyClassifier(nn.Module):
    def __init__(self):
        super().__init__()
        ...
 
    def forward(self, x):
        ...
        return x
 
 # create the skorch wrapper
 model = NeuralNetClassifier(
    module=MyClassifier
 )

NeuralNetClassifier 类的构造函数可以获得传递给 model.fit() 调用的参数（在 scikit-learn 模型中调用训练循环的方法），例如轮次数和批量大小等。 例如：

model = NeuralNetClassifier(
    module=MyClassifier,
    max_epochs=150,
    batch_size=10
 )

NeuralNetClassifier类的构造函数也可以接受新的参数，这些参数可以传递给你的模型类的构造函数，要求是必须在它前面加上module__(两个下划线)。这些新参数可能在构造函数中带有默认值，但当包装器实例化模型时，它们将被覆盖。例如:

import torch.nn as nn
 from skorch import NeuralNetClassifier
 
 class SonarClassifier(nn.Module):
    def __init__(self, n_layers=3):
        super().__init__()
        self.layers = []
        self.acts = []
        for i in range(n_layers):
            self.layers.append(nn.Linear(60, 60))
            self.acts.append(nn.ReLU())
            self.add_module(f"layer{i}", self.layers[-1])
            self.add_module(f"act{i}", self.acts[-1])
        self.output = nn.Linear(60, 1)
 
    def forward(self, x):
        for layer, act in zip(self.layers, self.acts):
            x = act(layer(x))
        x = self.output(x)
        return x
 
 model = NeuralNetClassifier(
    module=SonarClassifier,
    max_epochs=150,
    batch_size=10,
    module__n_layers=2
 )

我们可以通过初始化一个模型并打印来验证结果:

print(model.initialize())
 
 #结果如下：
 <class 'skorch.classifier.NeuralNetClassifier'>[initialized](
  module_=SonarClassifier(
    (layer0): Linear(in_features=60, out_features=60, bias=True)
    (act0): ReLU()
    (layer1): Linear(in_features=60, out_features=60, bias=True)
    (act1): ReLU()
    (output): Linear(in_features=60, out_features=1, bias=True)
  ),
 )

在scikit-learn中使用网格搜索

网格搜索是一种模型超参数优化技术。它只是简单地穷尽超参数的所有组合，并找到给出最佳分数的组合。在scikit-learn中，GridSearchCV类提供了这种技术。在构造这个类时，必须在param_grid参数中提供一个超参数字典。这是模型参数名和要尝试的值数组的映射。

默认使用精度作为优化的分数，但其他分数可以在GridSearchCV构造函数的score参数中指定。GridSearchCV将为每个参数组合构建一个模型进行评估。并且使用默认的3倍交叉验证，这些都是可以通过参数来进行设置的。

下面是定义一个简单网格搜索的例子:

param_grid = {
    'epochs': [10,20,30]
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, Y)

通过将GridSearchCV构造函数中的n_jobs参数设置为 -1表示将使用机器上的所有核心。否则，网格搜索进程将只在单线程中运行，这在多核cpu中较慢。

运行完毕就可以在grid.fit()返回的结果对象中访问网格搜索的结果。best_score提供了在优化过程中观察到的最佳分数，best_params_描述了获得最佳结果的参数组合。

示例问题描述

我们的示例都将在一个小型标准机器学习数据集上进行演示，该数据集是一个糖尿病发作分类数据集。这是一个小型数据集，所有的数值属性都很容易处理。

如何调优批大小和训练的轮次

在第一个简单示例中，我们将介绍如何调优批大小和拟合网络时使用的epoch数。

我们将简单评估从10到100的不批大小，代码清单如下所示:

import random
 import numpy as np
 import torch
 import torch.nn as nn
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 # PyTorch classifier
 class PimaClassifier(nn.Module):
    def __init__(self):
        super().__init__()
        self.layer = nn.Linear(8, 12)
        self.act = nn.ReLU()
        self.output = nn.Linear(12, 1)
        self.prob = nn.Sigmoid()
 
    def forward(self, x):
        x = self.act(self.layer(x))
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    optimizer=optim.Adam,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'batch_size': [10, 20, 40, 60, 80, 100],
    'max_epochs': [10, 50, 100]
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

结果如下:

Best: 0.714844 using {'batch_size': 10, 'max_epochs': 100}
 0.665365 (0.020505) with: {'batch_size': 10, 'max_epochs': 10}
 0.588542 (0.168055) with: {'batch_size': 10, 'max_epochs': 50}
 0.714844 (0.032369) with: {'batch_size': 10, 'max_epochs': 100}
 0.671875 (0.022326) with: {'batch_size': 20, 'max_epochs': 10}
 0.696615 (0.008027) with: {'batch_size': 20, 'max_epochs': 50}
 0.714844 (0.019918) with: {'batch_size': 20, 'max_epochs': 100}
 0.666667 (0.009744) with: {'batch_size': 40, 'max_epochs': 10}
 0.687500 (0.033603) with: {'batch_size': 40, 'max_epochs': 50}
 0.707031 (0.024910) with: {'batch_size': 40, 'max_epochs': 100}
 0.667969 (0.014616) with: {'batch_size': 60, 'max_epochs': 10}
 0.694010 (0.036966) with: {'batch_size': 60, 'max_epochs': 50}
 0.694010 (0.042473) with: {'batch_size': 60, 'max_epochs': 100}
 0.670573 (0.023939) with: {'batch_size': 80, 'max_epochs': 10}
 0.674479 (0.020752) with: {'batch_size': 80, 'max_epochs': 50}
 0.703125 (0.026107) with: {'batch_size': 80, 'max_epochs': 100}
 0.680990 (0.014382) with: {'batch_size': 100, 'max_epochs': 10}
 0.670573 (0.013279) with: {'batch_size': 100, 'max_epochs': 50}
 0.687500 (0.017758) with: {'batch_size': 100, 'max_epochs': 100}

可以看到’batch_size’: 10, ‘max_epochs’: 100达到了约71%的精度的最佳结果。

如何调整训练优化器

下面我们看看如何调整优化器，我们知道有很多个优化器可以选择比如SDG,Adam等，那么如何选择呢？

完整的代码如下:

import numpy as np
 import torch
 import torch.nn as nn
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 # PyTorch classifier
 class PimaClassifier(nn.Module):
    def __init__(self):
        super().__init__()
        self.layer = nn.Linear(8, 12)
        self.act = nn.ReLU()
        self.output = nn.Linear(12, 1)
        self.prob = nn.Sigmoid()
 
    def forward(self, x):
        x = self.act(self.layer(x))
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    max_epochs=100,
    batch_size=10,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'optimizer': [optim.SGD, optim.RMSprop, optim.Adagrad, optim.Adadelta,
                  optim.Adam, optim.Adamax, optim.NAdam],
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

输出如下:

Best: 0.721354 using {'optimizer': <class 'torch.optim.adamax.Adamax'>}
 0.674479 (0.036828) with: {'optimizer': <class 'torch.optim.sgd.SGD'>}
 0.700521 (0.043303) with: {'optimizer': <class 'torch.optim.rmsprop.RMSprop'>}
 0.682292 (0.027126) with: {'optimizer': <class 'torch.optim.adagrad.Adagrad'>}
 0.572917 (0.051560) with: {'optimizer': <class 'torch.optim.adadelta.Adadelta'>}
 0.714844 (0.030758) with: {'optimizer': <class 'torch.optim.adam.Adam'>}
 0.721354 (0.019225) with: {'optimizer': <class 'torch.optim.adamax.Adamax'>}
 0.709635 (0.024360) with: {'optimizer': <class 'torch.optim.nadam.NAdam'>}

可以看到对于我们的模型和数据集Adamax优化算法是最佳的，准确率约为72%。

如何调整学习率

虽然pytorch里面学习率计划可以让我们根据轮次动态调整学习率，但是作为样例，我们将学习率和学习率的参数作为网格搜索的一个参数来进行演示。在PyTorch中，设置学习率和动量的方法如下：

optimizer = optim.SGD(lr=0.001, momentum=0.9)

在skorch包中，使用前缀optimizer__将参数路由到优化器。

import numpy as np
 import torch
 import torch.nn as nn
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 # PyTorch classifier
 class PimaClassifier(nn.Module):
    def __init__(self):
        super().__init__()
        self.layer = nn.Linear(8, 12)
        self.act = nn.ReLU()
        self.output = nn.Linear(12, 1)
        self.prob = nn.Sigmoid()
 
    def forward(self, x):
        x = self.act(self.layer(x))
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    optimizer=optim.SGD,
    max_epochs=100,
    batch_size=10,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'optimizer__lr': [0.001, 0.01, 0.1, 0.2, 0.3],
    'optimizer__momentum': [0.0, 0.2, 0.4, 0.6, 0.8, 0.9],
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

结果如下：

Best: 0.682292 using {'optimizer__lr': 0.001, 'optimizer__momentum': 0.9}
 0.648438 (0.016877) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.0}
 0.671875 (0.017758) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.2}
 0.674479 (0.022402) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.4}
 0.677083 (0.011201) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.6}
 0.679688 (0.027621) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.8}
 0.682292 (0.026557) with: {'optimizer__lr': 0.001, 'optimizer__momentum': 0.9}
 0.671875 (0.019918) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.0}
 0.648438 (0.024910) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.2}
 0.546875 (0.143454) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.4}
 0.567708 (0.153668) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.6}
 0.552083 (0.141790) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.8}
 0.451823 (0.144561) with: {'optimizer__lr': 0.01, 'optimizer__momentum': 0.9}
 0.348958 (0.001841) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.0}
 0.450521 (0.142719) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.2}
 0.450521 (0.142719) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.4}
 0.450521 (0.142719) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.6}
 0.348958 (0.001841) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.8}
 0.348958 (0.001841) with: {'optimizer__lr': 0.1, 'optimizer__momentum': 0.9}
 0.444010 (0.136265) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.0}
 0.450521 (0.142719) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.2}
 0.348958 (0.001841) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.4}
 0.552083 (0.141790) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.6}
 0.549479 (0.142719) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.8}
 0.651042 (0.001841) with: {'optimizer__lr': 0.2, 'optimizer__momentum': 0.9}
 0.552083 (0.141790) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.0}
 0.348958 (0.001841) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.2}
 0.450521 (0.142719) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.4}
 0.552083 (0.141790) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.6}
 0.450521 (0.142719) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.8}
 0.450521 (0.142719) with: {'optimizer__lr': 0.3, 'optimizer__momentum': 0.9}

对于SGD，使用0.001的学习率和0.9的动量获得了最佳结果，准确率约为68%。

如何激活函数

激活函数控制单个神经元的非线性。我们将演示评估PyTorch中可用的一些激活函数。

import numpy as np
 import torch
 import torch.nn as nn
 import torch.nn.init as init
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 # PyTorch classifier
 class PimaClassifier(nn.Module):
    def __init__(self, activatinotallow=nn.ReLU):
        super().__init__()
        self.layer = nn.Linear(8, 12)
        self.act = activation()
        self.output = nn.Linear(12, 1)
        self.prob = nn.Sigmoid()
        # manually init weights
        init.kaiming_uniform_(self.layer.weight)
        init.kaiming_uniform_(self.output.weight)
 
    def forward(self, x):
        x = self.act(self.layer(x))
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    optimizer=optim.Adamax,
    max_epochs=100,
    batch_size=10,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'module__activation': [nn.Identity, nn.ReLU, nn.ELU, nn.ReLU6,
                            nn.GELU, nn.Softplus, nn.Softsign, nn.Tanh,
                            nn.Sigmoid, nn.Hardsigmoid]
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

结果如下：

Best: 0.699219 using {'module__activation': <class 'torch.nn.modules.activation.ReLU'>}
 0.687500 (0.025315) with: {'module__activation': <class 'torch.nn.modules.linear.Identity'>}
 0.699219 (0.011049) with: {'module__activation': <class 'torch.nn.modules.activation.ReLU'>}
 0.674479 (0.035849) with: {'module__activation': <class 'torch.nn.modules.activation.ELU'>}
 0.621094 (0.063549) with: {'module__activation': <class 'torch.nn.modules.activation.ReLU6'>}
 0.674479 (0.017566) with: {'module__activation': <class 'torch.nn.modules.activation.GELU'>}
 0.558594 (0.149189) with: {'module__activation': <class 'torch.nn.modules.activation.Softplus'>}
 0.675781 (0.014616) with: {'module__activation': <class 'torch.nn.modules.activation.Softsign'>}
 0.619792 (0.018688) with: {'module__activation': <class 'torch.nn.modules.activation.Tanh'>}
 0.643229 (0.019225) with: {'module__activation': <class 'torch.nn.modules.activation.Sigmoid'>}
 0.636719 (0.022326) with: {'module__activation': <class 'torch.nn.modules.activation.Hardsigmoid'>}

ReLU激活函数获得了最好的结果，准确率约为70%。

如何调整Dropout参数

在本例中，我们将尝试在0.0到0.9之间的dropout百分比(1.0没有意义)和在0到5之间的MaxNorm权重约束值。

import numpy as np
 import torch
 import torch.nn as nn
 import torch.nn.init as init
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 # PyTorch classifier
 class PimaClassifier(nn.Module):
    def __init__(self, dropout_rate=0.5, weight_cnotallow=1.0):
        super().__init__()
        self.layer = nn.Linear(8, 12)
        self.act = nn.ReLU()
        self.dropout = nn.Dropout(dropout_rate)
        self.output = nn.Linear(12, 1)
        self.prob = nn.Sigmoid()
        self.weight_constraint = weight_constraint
        # manually init weights
        init.kaiming_uniform_(self.layer.weight)
        init.kaiming_uniform_(self.output.weight)
 
    def forward(self, x):
        # maxnorm weight before actual forward pass
        with torch.no_grad():
            norm = self.layer.weight.norm(2, dim=0, keepdim=True).clamp(min=self.weight_constraint / 2)
            desired = torch.clamp(norm, max=self.weight_constraint)
            self.layer.weight *= (desired / norm)
        # actual forward pass
        x = self.act(self.layer(x))
        x = self.dropout(x)
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    optimizer=optim.Adamax,
    max_epochs=100,
    batch_size=10,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'module__weight_constraint': [1.0, 2.0, 3.0, 4.0, 5.0],
    'module__dropout_rate': [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

结果如下：

Best: 0.701823 using {'module__dropout_rate': 0.1, 'module__weight_constraint': 2.0}
 0.669271 (0.015073) with: {'module__dropout_rate': 0.0, 'module__weight_constraint': 1.0}
 0.692708 (0.035132) with: {'module__dropout_rate': 0.0, 'module__weight_constraint': 2.0}
 0.589844 (0.170180) with: {'module__dropout_rate': 0.0, 'module__weight_constraint': 3.0}
 0.561198 (0.151131) with: {'module__dropout_rate': 0.0, 'module__weight_constraint': 4.0}
 0.688802 (0.021710) with: {'module__dropout_rate': 0.0, 'module__weight_constraint': 5.0}
 0.697917 (0.009744) with: {'module__dropout_rate': 0.1, 'module__weight_constraint': 1.0}
 0.701823 (0.016367) with: {'module__dropout_rate': 0.1, 'module__weight_constraint': 2.0}
 0.694010 (0.010253) with: {'module__dropout_rate': 0.1, 'module__weight_constraint': 3.0}
 0.686198 (0.025976) with: {'module__dropout_rate': 0.1, 'module__weight_constraint': 4.0}
 0.679688 (0.026107) with: {'module__dropout_rate': 0.1, 'module__weight_constraint': 5.0}
 0.701823 (0.029635) with: {'module__dropout_rate': 0.2, 'module__weight_constraint': 1.0}
 0.682292 (0.014731) with: {'module__dropout_rate': 0.2, 'module__weight_constraint': 2.0}
 0.701823 (0.009744) with: {'module__dropout_rate': 0.2, 'module__weight_constraint': 3.0}
 0.701823 (0.026557) with: {'module__dropout_rate': 0.2, 'module__weight_constraint': 4.0}
 0.687500 (0.015947) with: {'module__dropout_rate': 0.2, 'module__weight_constraint': 5.0}
 0.686198 (0.006639) with: {'module__dropout_rate': 0.3, 'module__weight_constraint': 1.0}
 0.656250 (0.006379) with: {'module__dropout_rate': 0.3, 'module__weight_constraint': 2.0}
 0.565104 (0.155608) with: {'module__dropout_rate': 0.3, 'module__weight_constraint': 3.0}
 0.700521 (0.028940) with: {'module__dropout_rate': 0.3, 'module__weight_constraint': 4.0}
 0.669271 (0.012890) with: {'module__dropout_rate': 0.3, 'module__weight_constraint': 5.0}
 0.661458 (0.018688) with: {'module__dropout_rate': 0.4, 'module__weight_constraint': 1.0}
 0.669271 (0.017566) with: {'module__dropout_rate': 0.4, 'module__weight_constraint': 2.0}
 0.652344 (0.006379) with: {'module__dropout_rate': 0.4, 'module__weight_constraint': 3.0}
 0.680990 (0.037783) with: {'module__dropout_rate': 0.4, 'module__weight_constraint': 4.0}
 0.692708 (0.042112) with: {'module__dropout_rate': 0.4, 'module__weight_constraint': 5.0}
 0.666667 (0.006639) with: {'module__dropout_rate': 0.5, 'module__weight_constraint': 1.0}
 0.652344 (0.011500) with: {'module__dropout_rate': 0.5, 'module__weight_constraint': 2.0}
 0.662760 (0.007366) with: {'module__dropout_rate': 0.5, 'module__weight_constraint': 3.0}
 0.558594 (0.146610) with: {'module__dropout_rate': 0.5, 'module__weight_constraint': 4.0}
 0.552083 (0.141826) with: {'module__dropout_rate': 0.5, 'module__weight_constraint': 5.0}
 0.548177 (0.141826) with: {'module__dropout_rate': 0.6, 'module__weight_constraint': 1.0}
 0.653646 (0.013279) with: {'module__dropout_rate': 0.6, 'module__weight_constraint': 2.0}
 0.661458 (0.008027) with: {'module__dropout_rate': 0.6, 'module__weight_constraint': 3.0}
 0.553385 (0.142719) with: {'module__dropout_rate': 0.6, 'module__weight_constraint': 4.0}
 0.669271 (0.035132) with: {'module__dropout_rate': 0.6, 'module__weight_constraint': 5.0}
 0.662760 (0.015733) with: {'module__dropout_rate': 0.7, 'module__weight_constraint': 1.0}
 0.636719 (0.024910) with: {'module__dropout_rate': 0.7, 'module__weight_constraint': 2.0}
 0.550781 (0.146818) with: {'module__dropout_rate': 0.7, 'module__weight_constraint': 3.0}
 0.537760 (0.140094) with: {'module__dropout_rate': 0.7, 'module__weight_constraint': 4.0}
 0.542969 (0.138144) with: {'module__dropout_rate': 0.7, 'module__weight_constraint': 5.0}
 0.565104 (0.148654) with: {'module__dropout_rate': 0.8, 'module__weight_constraint': 1.0}
 0.657552 (0.008027) with: {'module__dropout_rate': 0.8, 'module__weight_constraint': 2.0}
 0.428385 (0.111418) with: {'module__dropout_rate': 0.8, 'module__weight_constraint': 3.0}
 0.549479 (0.142719) with: {'module__dropout_rate': 0.8, 'module__weight_constraint': 4.0}
 0.648438 (0.005524) with: {'module__dropout_rate': 0.8, 'module__weight_constraint': 5.0}
 0.540365 (0.136861) with: {'module__dropout_rate': 0.9, 'module__weight_constraint': 1.0}
 0.605469 (0.053083) with: {'module__dropout_rate': 0.9, 'module__weight_constraint': 2.0}
 0.553385 (0.139948) with: {'module__dropout_rate': 0.9, 'module__weight_constraint': 3.0}
 0.549479 (0.142719) with: {'module__dropout_rate': 0.9, 'module__weight_constraint': 4.0}
 0.595052 (0.075566) with: {'module__dropout_rate': 0.9, 'module__weight_constraint': 5.0}

可以看到，10%的Dropout和2.0的权重约束获得了70%的最佳精度。

如何调整隐藏层神经元的数量

单层神经元的数量是一个需要调优的重要参数。一般来说，一层神经元的数量控制着网络的表示能力，至少在拓扑的这一点上是这样。

理论上来说：由于通用逼近定理，一个足够大的单层网络可以近似任何其他神经网络。

在本例中，将尝试从1到30的值，步骤为5。一个更大的网络需要更多的训练，至少批大小和epoch的数量应该与神经元的数量一起优化。

import numpy as np
 import torch
 import torch.nn as nn
 import torch.nn.init as init
 import torch.optim as optim
 from skorch import NeuralNetClassifier
 from sklearn.model_selection import GridSearchCV
 
 # load the dataset, split into input (X) and output (y) variables
 dataset = np.loadtxt('pima-indians-diabetes.csv', delimiter=',')
 X = dataset[:,0:8]
 y = dataset[:,8]
 X = torch.tensor(X, dtype=torch.float32)
 y = torch.tensor(y, dtype=torch.float32).reshape(-1, 1)
 
 class PimaClassifier(nn.Module):
    def __init__(self, n_neurnotallow=12):
        super().__init__()
        self.layer = nn.Linear(8, n_neurons)
        self.act = nn.ReLU()
        self.dropout = nn.Dropout(0.1)
        self.output = nn.Linear(n_neurons, 1)
        self.prob = nn.Sigmoid()
        self.weight_constraint = 2.0
        # manually init weights
        init.kaiming_uniform_(self.layer.weight)
        init.kaiming_uniform_(self.output.weight)
 
    def forward(self, x):
        # maxnorm weight before actual forward pass
        with torch.no_grad():
            norm = self.layer.weight.norm(2, dim=0, keepdim=True).clamp(min=self.weight_constraint / 2)
            desired = torch.clamp(norm, max=self.weight_constraint)
            self.layer.weight *= (desired / norm)
        # actual forward pass
        x = self.act(self.layer(x))
        x = self.dropout(x)
        x = self.prob(self.output(x))
        return x
 
 # create model with skorch
 model = NeuralNetClassifier(
    PimaClassifier,
    criterinotallow=nn.BCELoss,
    optimizer=optim.Adamax,
    max_epochs=100,
    batch_size=10,
    verbose=False
 )
 
 # define the grid search parameters
 param_grid = {
    'module__n_neurons': [1, 5, 10, 15, 20, 25, 30]
 }
 grid = GridSearchCV(estimator=model, param_grid=param_grid, n_jobs=-1, cv=3)
 grid_result = grid.fit(X, y)
 
 # summarize results
 print("Best: %f using %s" % (grid_result.best_score_, grid_result.best_params_))
 means = grid_result.cv_results_['mean_test_score']
 stds = grid_result.cv_results_['std_test_score']
 params = grid_result.cv_results_['params']
 for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

结果如下：

Best: 0.708333 using {'module__n_neurons': 30}
 0.654948 (0.003683) with: {'module__n_neurons': 1}
 0.666667 (0.023073) with: {'module__n_neurons': 5}
 0.694010 (0.014382) with: {'module__n_neurons': 10}
 0.682292 (0.014382) with: {'module__n_neurons': 15}
 0.707031 (0.028705) with: {'module__n_neurons': 20}
 0.703125 (0.030758) with: {'module__n_neurons': 25}
 0.708333 (0.015733) with: {'module__n_neurons': 30}

你可以看到，在隐藏层中有30个神经元的网络获得了最好的结果，准确率约为71%。

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