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UtilityFunction

Predict，Classify，およびその関連関数のオプションであり，実際の値と予測値の可能なペアそれぞれに割り当てる効用の値を指定する．

詳細
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例題  
例  
スコープ  
アプリケーション  
特性と関係  
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UtilityFunction

UtilityFunction

Predict，Classify，およびその関連関数のオプションであり，実際の値と予測値の可能なペアそれぞれに割り当てる効用の値を指定する．

詳細

  • UtilityFunctionf とすると，実際の値 vaと予測値 vpに割り当てられた効用の値は f[va,vp]であるとされる．
  • Classifyの場合には，f は通常<|class1<|class1u11,class2u12…|>,…|>の形を持つ，連想の連想である．ここで，uijは，i が実際のクラス，j が予測クラスを表す効用行列である．

例題

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例  (2)

分類器を訓練する：

Wolfram Language code: c = Classify[{0 -> "healthy", 1 -> "healthy", 2 -> "diseased", 3 -> "healthy", 4 -> "diseased", 5 -> "diseased"}]

新たな例については，もっとも可能性の高いクラスが予測される：

Wolfram Language code: c[1.5, "Probabilities"]
Wolfram Language code: c[1.5]

決定効用を設定し，クラス"diseased"を"healthy"とする誤判別にペナルティを課す：

Wolfram Language code: c[1.5, UtilityFunction -> <| "healthy" -> <|"healthy" -> 1, "diseased" -> 0|>, "diseased" -> <|"healthy" -> -3, "diseased" -> 1|> |>]

予測器を訓練する：

Wolfram Language code: p = Predict[{1 -> 2.2, 2 -> 4.4, 3 -> 5.5, 4 -> 7.7, 5 -> 9.4}]

デフォルトで，最も高い確率密度の値が予測される：

Wolfram Language code: p[4]

予測された値が実際の値よりも小さかった場合にペナルティを課す効用関数を設定する：

Wolfram Language code: p[4, UtilityFunction -> Function[{actual, prediction}, -Piecewise[{{Exp[prediction - actual], actual < prediction}, {Exp[3 * (actual - prediction)], actual ≥ prediction}}] ]]

スコープ  (7)

分類器の訓練でUtilityFunctionを設定する：

Wolfram Language code: c = Classify[{0 -> "healthy", 1 -> "healthy", 2 -> "diseased", 3 -> "healthy", 4 -> "diseased", 5 -> "diseased"}, UtilityFunction -> <| "healthy" -> <|"healthy" -> 1, "diseased" -> 0|>, "diseased" -> <|"healthy" -> -3, "diseased" -> 1|> |>]

分類を取得する：

Wolfram Language code: c[1.5]

ClassifierFunctionからUtilityFunctionを抽出する：

Wolfram Language code: Information[ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... te" -> DateObject[{2026, 2, 5, 14, 28, 25.083556`8.151964087135537}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]], UtilityFunction]

Indeterminate決定確率（オプションIndeterminateThresholdからは独立した）を含む効用関数を使う：

Wolfram Language code: ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... te" -> DateObject[{2026, 2, 5, 14, 28, 25.083556`8.151964087135537}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]][1.5, UtilityFunction -> <| "healthy" -> <|"healthy" -> 1, "diseased" -> 0, Indeterminate -> 0.8|>, "diseased" -> <|"healthy" -> 0, "diseased" -> 1, Indeterminate -> 0.9|> |>]

UtilityFunction値が修正された，新たなClassifierFunctionを取得する：

Wolfram Language code: Classify[ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... te" -> DateObject[{2026, 2, 5, 14, 28, 25.083556`8.151964087135537}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]], UtilityFunction -> <| "healthy" -> <|"healthy" -> 1, "diseased" -> 0|>, "diseased" -> <|"healthy" -> 0, "diseased" -> 1|> |>]

予測器の訓練でUtilityFunctionを設定する：

Wolfram Language code: p = Predict[{1 -> 2.2, 2 -> 4.4, 3 -> 5.5, 4 -> 7.7, 5 -> 9.4}, UtilityFunction -> Function[{actual, prediction}, -Piecewise[{{Exp[prediction - actual], actual < prediction}, {Exp[3 * (actual - prediction)], actual ≥ prediction}}] ]]

予測を取得する：

Wolfram Language code: p[4]

PredictorFunctionから現行のUtilityFunction値を抽出する：

Wolfram Language code: Information[PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... te" -> DateObject[{2026, 2, 5, 14, 32, 38.007625`8.332445711286626}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]], UtilityFunction]

UtilityFunction値が修正された，新たなPredictorFunctionを取得する：

Wolfram Language code: Predict[PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... te" -> DateObject[{2026, 2, 5, 14, 32, 38.007625`8.332445711286626}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]], UtilityFunction -> Function[DiracDelta[#2 - #1]]]

アプリケーション  (1)

訓練集合および"Mushroom"データ集合の検定集合をロードする：

Wolfram Language code: trainingset = ExampleData[{"MachineLearning", "Mushroom"}, "TrainingData"];
Wolfram Language code: testset = ExampleData[{"MachineLearning", "Mushroom"}, "TestData"];

訓練集合の部分について分類器を訓練する：

Wolfram Language code: c = Classify[RandomSample[trainingset, 100]]

分類器の検定集合についての混同行列を可視化する：

Wolfram Language code: ClassifierMeasurements[c, testset, "ConfusionMatrixPlot"]

分類器がUtilityFunctionの異なる値を有する場合に得られた，混同行列を可視化する：

Wolfram Language code: utility = <| "edible" -> <|"edible" -> 1, "poisonous" -> 0, Indeterminate -> 0.5|>, "poisonous" -> <|"edible" -> -10, "poisonous" -> 1, Indeterminate -> 0.8|> |>;
Wolfram Language code: ClassifierMeasurements[c, testset, "ConfusionMatrixPlot", UtilityFunction -> utility]

特性と関係  (4)

ClassifierFunctionについてのデフォルトの効用関数の値は恒等行列である：

Wolfram Language code: Information[Classify[{0 -> "healthy", 1 -> "healthy", 2 -> "diseased", 3 -> "healthy", 4 -> "diseased", 5 -> "diseased"}], UtilityFunction]

分類決定は期待される効用を最大にする：

Wolfram Language code: ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... te" -> DateObject[{2026, 2, 5, 14, 50, 41.562291`8.371274456737947}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]][1.5, "ExpectedUtilities", UtilityFunction -> <| "diseased" -> <|"diseased" -> 1, "healthy" -> -3, Indeterminate -> 0.1|>, "healthy" -> <| "diseased" -> 0, "healthy" -> 1, Indeterminate -> 0.1|> |>]
Wolfram Language code: ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], ... te" -> DateObject[{2026, 2, 5, 14, 50, 41.562291`8.371274456737947}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]][1.5, UtilityFunction -> <| "diseased" -> <|"diseased" -> 1, "healthy" -> -3, Indeterminate -> 0.1|>, "healthy" -> <| "diseased" -> 0, "healthy" -> 1, Indeterminate -> 0.1|> |>]

期待されるん効用は，予測される確率による効用値の積である：

Wolfram Language code: {{1., -3, 0.1}, {0., 1., 0.1}}.Lookup[c[1.5, "Probabilities"], {"diseased", "healthy"}]

PredictorFunctionについてのデフォルトの効用関数の値はディラック(Dirac)のデルタ関数である：

Wolfram Language code: Information[Predict[{1 -> 2.2, 2 -> 4.4, 3 -> 5.5, 4 -> 7.7, 5 -> 9.4}], UtilityFunction]

PredictorFunction予測は期待される効用を最大にする：

Wolfram Language code: Predict[{1 -> 2.2, 2 -> 4.4, 3 -> 5.5, 4 -> 7.7, 5 -> 9.4}][4, UtilityFunction -> Function[{actual, prediction}, -Piecewise[{{Exp[prediction - actual], actual < prediction}, {Exp[3 * (actual - prediction)], actual ≥ prediction}}] ]]
Wolfram Research (2014), UtilityFunction, Wolfram言語関数， https://reference.wolfram.com/language/ref/UtilityFunction.html.

テキスト

Wolfram Research (2014), UtilityFunction, Wolfram言語関数， https://reference.wolfram.com/language/ref/UtilityFunction.html.

CMS

Wolfram Language. 2014. "UtilityFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UtilityFunction.html.

APA

Wolfram Language. (2014). UtilityFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UtilityFunction.html

BibTeX

@misc{reference.wolfram_2026_utilityfunction, author="Wolfram Research", title="{UtilityFunction}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/UtilityFunction.html}", note=[Accessed: 01-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_utilityfunction, organization={Wolfram Research}, title={UtilityFunction}, year={2014}, url={https://reference.wolfram.com/language/ref/UtilityFunction.html}, note=[Accessed: 01-November-2026]}