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如何使用scikit-learn為PyTorch模型進行超參數網格搜尋?

PHPz
PHPz轉載
2023-04-20 20:13:061719瀏覽

使用scikit-learn为PyTorch 模型进行超参数网格搜索

scikit-learn是Python中最好的機器學習函式庫,而PyTorch又為我們建構模型提供了方便的操作,能否將它們的優點整合起來呢?在本文中,我們將介紹如何使用scikit-learn中的網格搜尋功能來調整PyTorch 深度學習模型的超參數:

  • 如何包裝PyTorch 模型以用於scikit-learn 以及如何使用網格搜尋
  • 如何網格搜尋常見的神經網路參數,如學習率、Dropout、epochs、神經元數
  • 在自己的專案上定義自己的超參數調優實驗

如何在scikit-learn 中使用PyTorch 模型

#要讓PyTorch 模型可以在scikit-learn 中使用的一個最簡單的方法是使用skorch套件。這個套件為 PyTorch 模型提供與 scikit-learn 相容的 API。在skorch中,有分類神經網路的NeuralNetClassifier和回歸神經網路的NeuralNetRegressor。

pip install skorch

要使用這些包裝器,必須使用 nn.Module 將 PyTorch 模型定義為類,然後在建構 NeuralNetClassifier 類別時將類別的名稱傳遞給模組參數。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 類別的建構子可以獲得傳遞給 model.fit() 呼叫的參數(在 scikit-learn 模型中呼叫訓練循環的方法),例如輪次數和批次大小等。例如:

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

NeuralNetClassifier類別的建構子也可以接受新的參數,這些參數可以傳遞給你的模型類別的建構函數,要求是必須在它前面加上module__(兩個下劃線)。這些新參數可能在建構函數中帶有預設值,但當包裝器實例化模型時,它們將被覆寫。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
 )

我們可以透過初始化一個模型並列印來驗證結果:

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中使用網格搜尋

網格搜尋是一種模型超參數優化技術。它只是簡單地窮盡超參數的所有組合,並找到給出最佳分數的組合。在scikit-learn中,GridSearchCV類別提供了這種技術。在建構這個類別時,必須在param_grid參數中提供一個超參數字典。這是模型參數名稱和要嘗試的值數組的映射。

預設使用精確度作為最佳化的分數,但其他分數可以在GridSearchCV建構子的score參數中指定。 GridSearchCV將為每個參數組合建立一個模型進行評估。並且使用預設的3倍交叉驗證,這些都是可以透過參數來進行設定的。

下面是定義一個簡單網格搜尋的範例:

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)

透過將GridSearchCV建構函式中的n_jobs參數設定為 -1表示將使用機器上的所有核心。否則,網格搜尋進程將只在單執行緒中運行,這在多核心cpu中較慢。

運行完畢就可以在grid.fit()傳回的結果物件中存取網格搜尋的結果。 best_score提供了在最佳化過程中觀察到的最佳分數,best_params_描述了獲得最佳結果的參數組合。

範例問題描述

我們的範例都將在一個小型標準機器學習資料集上進行演示,該資料集是一個糖尿病發作分類資料集。這是一個小型資料集,所有的數值屬性都很容易處理。

如何調優批次大小和訓練的輪次

在第一個簡單範例中,我們將介紹如何調優批次大小和擬合網路時使用的epoch數。

我們將簡單評估從10到100的不批大小,程式碼清單如下所示:

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))

結果如下:

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達到了約71%的精度的最佳結果。

如何調整訓練優化器

下面我們來看看如何調整最佳化器,我們知道有很多個最佳化器可以選擇像是SDG,Adam等,那麼如何選擇呢?

完整的程式碼如下:

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))

輸出如下:

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'>}

#可以看到對於我們的模型和資料集Adamax最佳化演算法是最佳的,準確率約為72%。

如何調整學習率

雖然pytorch裡面學習率計畫可以讓我們根據輪次動態調整學習率,但是作為範例,我們將學習率和學習率的參數作為網格搜尋的一個參數來進行示範。在PyTorch中,設定學習率和動量的方法如下:

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

在skorch套件中,使用前綴optimizer__將參數路由到優化器。

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))

結果如下:

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}

對於SGD,使用0.001的學習率和0.9的動量獲得了最佳結果,準確率約為68%。

如何活化函數

激活函數控制單一神經元的非線性。我們將示範評估PyTorch中可用的一些激活函數。

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))

結果如下:

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激活函數獲得了最好的結果,準確率約為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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