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UtilityFunction

是 Predict、Classify 和相关函数的一个选项，指定分配给每个可能的实际和预测值对的效用值.

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UtilityFunction

UtilityFunction

是 Predict、Classify 和相关函数的一个选项，指定分配给每个可能的实际和预测值对的效用值.

更多信息

  • 设置 UtilityFunctionf 下，分配给实际值 va 和预测值 vp 的效用值是 f[va,vp].
  • 在 Classify 的情况下，f 通常使相关性组成的相关性，格式为 <|class1<|class1u11,class2u12…|>,…|>. 其中 uij 是效用矩阵，而 i 是实际类别，j 是预测类别.

范例

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基本范例  (2)

训练一个分类器：

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

对于一个新的范例，预测最可能的分类：

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

将决策效用设置为惩罚将 "diseased" 类成员误分类为 "healthy" 的情况：

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

训练一个预测器：

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

默认情况下，会预测概率密度最高的值：

Wolfram Language code: p[4]

设置一个效用函数，用于惩罚预测值小于实际值的情况：

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

范围  (7)

设置分类器训练时使用的 UtilityFunction：

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|> |>]

获取分类：

Wolfram Language code: c[1.5]

从 ClassifierFunction 中提取 UtilityFunction：

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]

使用一个包含 Indeterminate 决策可能性（独立于选项 IndeterminateThreshold）的效用函数：

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|> |>]

修改 UtilityFunction 的值，获取新的 ClassifierFunction：

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|> |>]

设置预测器训练时使用的 UtilityFunction：

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}}] ]]

获取预测：

Wolfram Language code: p[4]

从 PredictorFunction 中提取 UtilityFunction 当前的值：

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]

修改 UtilityFunction 的值，获取新的 PredictorFunction：

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]]]

应用  (1)

加载 "Mushroom" 数据集的训练集合和测试集合：

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

在训练集合的一部分上训练一个分类器：

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

可视化测试集合上分类器的混淆矩阵：

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

当分类器有一个不同的 UtilityFunction 值时，可视化获得的混淆矩阵：

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]

属性和关系  (4)

ClassifierFunction 的默认效用函数值为单位矩阵：

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

分类决策旨在最大化期望的效用值：

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|> |>]

期望效用是效用值与其预测概率的乘积：

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

PredictorFunction 的默认效用函数值为 Dirac delta 函数：

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

PredictorFunction 的预测旨在最大化期望的效用值：

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 语言函数，https://reference.wolfram.com/language/ref/UtilityFunction.html.

文本

Wolfram Research (2014)，UtilityFunction，Wolfram 语言函数，https://reference.wolfram.com/language/ref/UtilityFunction.html.

CMS

Wolfram 语言. 2014. "UtilityFunction." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/UtilityFunction.html.

APA

Wolfram 语言. (2014). UtilityFunction. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/UtilityFunction.html 年

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: 09-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: 09-November-2026]}