Wolfram 语言

神经网络

用验证集来避免过度拟合

使用 NetTrainValidationSet 选项以保证训练过的网络不对输入数据做过度拟合.

创建基于高斯曲线的合成训练数据.

In[1]:=
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data = Table[ x -> Exp[-x^2] + RandomVariate[NormalDistribution[0, .15]], {x, -3, 3, .2}];
In[2]:=
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plot = ListPlot[List @@@ data, PlotStyle -> Red]
Out[2]=

训练一个相对于训练数据具有大量参数的网络.

In[3]:=
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net = NetChain[{150, Tanh, 150, Tanh, 1}, "Input" -> "Scalar", "Output" -> "Scalar"]; net1 = NetTrain[net, data, Method -> "ADAM"]
In[4]:=
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"RGB", Interleaving -> True, Magnification -> 0.5], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSize->Magnification[0.5], ImageSizeRaw->{560, 706}, PlotRange->{{0, 560}, {0, 706}}]\)

由此产生的网络会过度拟合数据,除了基本函数外还学习噪声.

In[5]:=
Click for copyable input
Show[Plot[net1[x], {x, -3, 3}], plot]
Out[5]=

将数据细分为一个训练集和一个留出的验证集.

In[6]:=
Click for copyable input
data = RandomSample[data]; {train, test} = TakeDrop[data, 24];

使用 ValidationSet 选项,使得 NetTrain 在训练中选择取得最低验证损失的网络.

In[7]:=
Click for copyable input
net2 = NetTrain[net, train, ValidationSet -> test]
In[8]:=
Click for copyable input
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如验证损失所示,由 NetTrain 返回的结果是向验证集中的点做了最佳推广的网络. 这会惩罚过度拟合,因为训练数据中的噪声与验证集中的噪音是不相关的.

In[9]:=
Click for copyable input
Show[Plot[net2[x], {x, -3, 3}], plot]
Out[9]=

解决过拟合的另一种方法是使用 L2 正规化,该方法在网络训练时隐式地将损失与非零参数关联起来. 这可以在 NetTrain 中用一个 Method 选项来设定.

In[10]:=
Click for copyable input
net3 = NetTrain[net, data, Method -> {"ADAM", "L2Regularization" -> 5}]
Out[10]=

L2 正规化惩罚复杂的网,由其参数的大小来衡量. 这往往可以降低过拟合.

In[11]:=
Click for copyable input
Show[Plot[net3[x], {x, -3, 3}], plot]
Out[11]=

相关范例

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