ホールドアウト集合を使って,過剰適合を避ける
NetTrainでValidationSetオプションを使って,訓練されたネットワークが入力データに過剰適合しないようにする.これは通常テストデータ集合またはホールドアウトデータ集合と呼ばれる.
ガウス曲線に基づいた合成訓練データを生成する.
In[1]:=
data = Table[
x -> Exp[-x^2] + RandomVariate[NormalDistribution[0, .15]], {x, -3,
3, .2}];
In[2]:=
plot = ListPlot[List @@@ data, PlotStyle -> Red]
Out[2]=
訓練データの量に対して多数のパラメータを持つネットワークを訓練する.
In[3]:=
net = NetChain[{150, Tanh, 150, Tanh, 1}, "Input" -> "Scalar",
"Output" -> "Scalar"];
net1 = NetTrain[net, data, Method -> "ADAM"]
Out[3]=
In[4]:=
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BoxForm`ImageTag[
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結果のネットワークはデータに過剰適合し,潜在する関数の他にノイズも学習する.
In[5]:=
Show[Plot[net1[x], {x, -3, 3}], plot]
Out[5]=
データを訓練集合とホールドアウト検証集合に分ける.
In[6]:=
data = RandomSample[data];
{train, test} = TakeDrop[data, 24];
ValidationSetオプションを使って,NetTrainに訓練中に最低の検証損失を記録したネットワークを選ばせる.
In[7]:=
net2 = NetTrain[net, train, ValidationSet -> test]
Out[7]=
In[8]:=
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"], {{0, 750}, {562, 0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag[
"Byte", ColorSpace -> "RGB", Interleaving -> True,
Magnification -> 0.5],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Magnification[0.5],
ImageSizeRaw->{562, 750},
PlotRange->{{0, 562}, {0, 750}}]\)
NetTrainによって返された結果は,検証損失として測定されたように,検証集合の点に最もよく一般化されたネットワークであった.訓練データに存在したノイズは検証集合に存在したノイズとは無関係なので,これは過剰適合にペナルティを課すことになる.
In[9]:=
Show[Plot[net2[x], {x, -3, 3}], plot]
Out[9]=
過剰適合に対処する別の方法として,訓練中に損失をネットワークの中の非零のパラメータと陰的に関連付けるL2正規化を使うというものがある.これはNetTrainのMethodオプションで指定することができる.
In[10]:=
net3 = NetTrain[net, data,
Method -> {"ADAM", "L2Regularization" -> 0.01}]
Out[10]=
L2正規化は,パラメータの大きさによって測定される「複雑な」ネットワークにペナルティを課すもので,これは過剰適合を減らす傾向がある.
In[11]:=
Show[Plot[net3[x], {x, -3, 3}], plot]
Out[11]=