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RecalibrationFunction

is an option for Classify, Predict and related functions that specifies how to post-process model predictions.

Details

For classifiers, recalibration is also known as probability calibration and is typically used to correct overconfident or underconfident classifiers.
RecalibrationFunction can be used at training time, inference time or to update the calibrator of an existing model.
When specified at inference time or to update the calibrator of an existing model, typical settings for RecalibrationFunction include:
None remove existing recalibration

f append the function f to the existing calibrator
For classifiers, the function f is applied to the class probabilities f[<|class₁p₁,class₂p₂,…|>] and should return new class probabilities. New class probabilities are automatically normalized.
For predictors, the function f transforms the predictive distribution by being applied to the output values.
When specified at training time, typical settings for RecalibrationFunction include:
None prevent any recalibration

Automatic recalibrate the model when needed

All always recalibrate the model
Besides being used on the final model, recalibration is also applied to candidate models generated by Classify and Predict during their training procedure.
When RecalibrationFunctionAll, recalibration is applied to every candidate model.
When RecalibrationFunctionAutomatic, recalibration is only used for candidate models that need it.

Examples

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Basic Examples (2)

Train a classifier without any recalibration:

Wolfram Language code: c = Classify[{1 -> "A", 2 -> "A", 3.5 -> "B", 3.7 -> "A", 4 -> "B", 5.5 -> "B"}, RecalibrationFunction -> None]

Compute the class probabilities of a new example:

Wolfram Language code: c[3, "Probabilities"]

Temporarily set a recalibration function to apply to the probabilities:

Wolfram Language code: c[3, "Probabilities", RecalibrationFunction -> Sqrt]

Train a predictor without any recalibration:

Wolfram Language code: p = Predict[{1 -> 1.3, 2 -> 2.4, 3 -> 4.4, 4 -> 5.1, 6 -> 7.3}, RecalibrationFunction -> None]

Compute the predictive distribution:

Wolfram Language code: p[3.4, "Distribution"]

Compute the predictive distribution with a temporary set recalibration function:

Wolfram Language code: p[3.4, "Distribution", RecalibrationFunction -> (.5# + 0.1&)]

Scope (12)

Training (6)

Train a ClassifierFunction with recalibration if needed (default):

Wolfram Language code:

c = Classify[{1 -> "A", 2 -> "A", 3.5 -> "B", 3.7 -> "A", 4 -> "B", 5.5 -> "B"}, Method -> "RandomForest", RecalibrationFunction -> Automatic]

Check if the model has been calibrated:

Wolfram Language code: Information[c, "Calibrated"]

Compute the class probabilities of a new example:

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

Compare with the raw random forest model probabilities:

Wolfram Language code: c[1.5, "Probabilities", RecalibrationFunction -> None]

Train a ClassifierFunction with no recalibration:

Wolfram Language code:

c = Classify[{1 -> "A", 2 -> "A", 3.5 -> "B", 3.7 -> "A", 4 -> "B", 5.5 -> "B"}, Method -> "RandomForest", RecalibrationFunction -> None]

Train a ClassifierFunction with mandatory recalibration:

Wolfram Language code:

c = Classify[{1 -> "A", 2 -> "A", 3.5 -> "B", 3.7 -> "A", 4 -> "B", 5.5 -> "B"}, Method -> "LogisticRegression", RecalibrationFunction -> All]

Compute the class probabilities of a new example:

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

Compare with the raw logistic regression model probabilities:

Wolfram Language code: c[1.5, "Probabilities", RecalibrationFunction -> None]

Train a PredictorFunction with recalibration if needed (default):

Wolfram Language code:

p = Predict[{0 -> 0.94, 0.10 -> 0.67, 0.20 -> 0.60, 0.30 -> 0.47, 0.40 -> 0.41, 0.50 -> 1.2, 0.60 -> 0.87, 0.70 -> 1.5, 0.80 -> 1.8, 0.90 -> 1.9, 1.0 -> 1.2, 1.1 -> 1.5, 1.2 -> 1.9, 1.3 -> 1.5, 1.4 -> 1.7, 1.5 -> 2.3, 1.6 -> 2.0, 1.7 -> 2.2, 1.8 -> 2.0, 1.9 -> 2.8, 2.0 -> 2.7, 2.1 -> 2.5, 2.2 -> 2.6, 2.3 -> 2.7, 2.4 -> 2.5, 2.5 -> 3.1, 2.6 -> 2.6, 2.7 -> 2.9, 2.8 -> 3.0, 2.9 -> 3.7, 3.0 -> 3.4, 3.1 -> 4.0, 3.2 -> 3.9, 3.3 -> 4.3, 3.4 -> 4.0, 3.5 -> 4.0, 3.6 -> 4.1, 3.7 -> 4.1, 3.8 -> 4.5, 3.9 -> 4.4, 4.0 -> 4.2, 4.1 -> 4.9, 4.2 -> 5.2, 4.3 -> 4.4, 4.4 -> 4.4, 4.5 -> 5.1, 4.6 -> 5.1, 4.7 -> 5.3, 4.8 -> 5.1, 4.9 -> 5.4, 5.0 -> 5.9}, Method -> "LinearRegression", RecalibrationFunction -> Automatic]

Check if the model has been calibrated:

Wolfram Language code: Information[p, "Calibrated"]

Compute the class probabilities of a new example:

Wolfram Language code: p[2.5, "Distribution"]

Train a PredictorFunction with no recalibration:

Wolfram Language code:

p = Predict[{0 -> 0.94, 0.10 -> 0.67, 0.20 -> 0.60, 0.30 -> 0.47, 0.40 -> 0.41, 0.50 -> 1.2, 0.60 -> 0.87, 0.70 -> 1.5, 0.80 -> 1.8, 0.90 -> 1.9, 1.0 -> 1.2, 1.1 -> 1.5, 1.2 -> 1.9, 1.3 -> 1.5, 1.4 -> 1.7, 1.5 -> 2.3, 1.6 -> 2.0, 1.7 -> 2.2, 1.8 -> 2.0, 1.9 -> 2.8, 2.0 -> 2.7, 2.1 -> 2.5, 2.2 -> 2.6, 2.3 -> 2.7, 2.4 -> 2.5, 2.5 -> 3.1, 2.6 -> 2.6, 2.7 -> 2.9, 2.8 -> 3.0, 2.9 -> 3.7, 3.0 -> 3.4, 3.1 -> 4.0, 3.2 -> 3.9, 3.3 -> 4.3, 3.4 -> 4.0, 3.5 -> 4.0, 3.6 -> 4.1, 3.7 -> 4.1, 3.8 -> 4.5, 3.9 -> 4.4, 4.0 -> 4.2, 4.1 -> 4.9, 4.2 -> 5.2, 4.3 -> 4.4, 4.4 -> 4.4, 4.5 -> 5.1, 4.6 -> 5.1, 4.7 -> 5.3, 4.8 -> 5.1, 4.9 -> 5.4, 5.0 -> 5.9}, Method -> "LinearRegression", RecalibrationFunction -> None]

Train a PredictorFunction with mandatory recalibration:

Wolfram Language code:

p = Predict[{0 -> 0.94, 0.10 -> 0.67, 0.20 -> 0.60, 0.30 -> 0.47, 0.40 -> 0.41, 0.50 -> 1.2, 0.60 -> 0.87, 0.70 -> 1.5, 0.80 -> 1.8, 0.90 -> 1.9, 1.0 -> 1.2, 1.1 -> 1.5, 1.2 -> 1.9, 1.3 -> 1.5, 1.4 -> 1.7, 1.5 -> 2.3, 1.6 -> 2.0, 1.7 -> 2.2, 1.8 -> 2.0, 1.9 -> 2.8, 2.0 -> 2.7, 2.1 -> 2.5, 2.2 -> 2.6, 2.3 -> 2.7, 2.4 -> 2.5, 2.5 -> 3.1, 2.6 -> 2.6, 2.7 -> 2.9, 2.8 -> 3.0, 2.9 -> 3.7, 3.0 -> 3.4, 3.1 -> 4.0, 3.2 -> 3.9, 3.3 -> 4.3, 3.4 -> 4.0, 3.5 -> 4.0, 3.6 -> 4.1, 3.7 -> 4.1, 3.8 -> 4.5, 3.9 -> 4.4, 4.0 -> 4.2, 4.1 -> 4.9, 4.2 -> 5.2, 4.3 -> 4.4, 4.4 -> 4.4, 4.5 -> 5.1, 4.6 -> 5.1, 4.7 -> 5.3, 4.8 -> 5.1, 4.9 -> 5.4, 5.0 -> 5.9}, Method -> "LinearRegression", RecalibrationFunction -> All]

Compute the probability distribution for a new example:

Wolfram Language code: p[2.5, "Distribution"]

Compare with the raw logistic regression model probabilities:

Wolfram Language code: p[2.5, "Distribution", RecalibrationFunction -> None]

Inference (6)

Compute the class probabilities of a example without recalibration:

Wolfram Language code:

ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Probabilities", RecalibrationFunction -> None]

Use the build in recalibration function:

Wolfram Language code:

ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Probabilities"]

Temporarily set a custom recalibration function after the classifier built-in one:

Wolfram Language code:

ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Probabilities", RecalibrationFunction -> Sqrt]

Obtain a new ClassifierFunction with a removed calibration:

Wolfram Language code:

c = Classify[ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]], RecalibrationFunction -> None]

Wolfram Language code: Information[c, "Calibrated"]

Obtain a new ClassifierFunction appending a custom function to the calibrator:

Wolfram Language code:

c = Classify[ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]], RecalibrationFunction -> Sqrt]

Compute the predicted probability distribution for an example without recalibration:

Wolfram Language code:

PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 9, 
       21.546464`8.085950991511702}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][2.5, "Distribution", RecalibrationFunction -> None]

Use the PredictorFunction built-in recalibration function:

Wolfram Language code:

PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 9, 
       21.546464`8.085950991511702}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][2.5, "Distribution"]

Temporarily set a custom recalibration function after the PredictorFunction built-in one:

Wolfram Language code:

PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 9, 
       21.546464`8.085950991511702}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][2.5, "Distribution", RecalibrationFunction -> (.5# + 0.1&)]

Obtain a new PredictorFunction with a removed calibration:

Wolfram Language code:

p = Predict[PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 9, 
       21.546464`8.085950991511702}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]], RecalibrationFunction -> None]

Wolfram Language code: Information[p, "Calibrated"]

Obtain a new PredictorFunction appending a custom function to the calibrator:

Wolfram Language code:

p = Predict[PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 9, 
       21.546464`8.085950991511702}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]], RecalibrationFunction -> (.5# + 0.1&)]

Applications (3)

MNIST (1)

Load the MNIST dataset:

Wolfram Language code:

training = RandomSample[ResourceData["MNIST", "TrainingData"], 1000];
test = ResourceData["MNIST", "TestData"];

Train a random forest classifier without any recalibration:

Wolfram Language code: c = Classify[training, Method -> "RandomForest", RecalibrationFunction -> None]

Visualize the calibration curve on a test set:

Wolfram Language code: ClassifierMeasurements[c, test, "CalibrationCurve"]

Train a random forest classifier with recalibration:

Wolfram Language code: c2 = Classify[training, Method -> "RandomForest", RecalibrationFunction -> All]

Visualize the calibration curve on a test set:

Wolfram Language code: ClassifierMeasurements[c2, test, "CalibrationCurve"]

Titanic (1)

Load the Titanic dataset:

Wolfram Language code:

train  = ExampleData[{"MachineLearning", "Titanic"}, "TrainingData"]; 
test = ExampleData[{"MachineLearning", "Titanic"}, "TestData"];

Train a nearest neighbors classifier with no calibration function:

Wolfram Language code: c = Classify[train, Method -> "NearestNeighbors", RecalibrationFunction -> None]

The classifier is slightly overconfident:

Wolfram Language code: ClassifierMeasurements[c, test, "CalibrationCurve"]

Select the worst classification case in the test set:

Wolfram Language code: badcase = First@ClassifierMeasurements[c, test, "WorstClassifiedExamples" -> 1]

Evaluate the estimated probabilities:

Wolfram Language code: c[badcase[[1]], "Probabilities"]

Use "temperature scaling" to reduce the classifier self-confidence:

Wolfram Language code: c[badcase[[1]], "Probabilities", RecalibrationFunction -> (# ^ .8&)]

Wolfram Language code: ClassifierMeasurements[Classify[c, RecalibrationFunction -> (# ^ .8&)], test, "CalibrationCurve"]

Boston Homes (1)

Load the Boston Homes dataset:

Wolfram Language code:

training = RandomSample[ResourceData["Sample Data: Boston Homes", "TrainingData"]];
test = ResourceData["Sample Data: Boston Homes", "TestData"];

Train a predictor with model calibration:

Wolfram Language code: p = Predict[training, Method -> "RandomForest", RecalibrationFunction -> All]

Visualize the comparison plot on a test set:

Wolfram Language code: PredictorMeasurements[p, test, "ComparisonPlot"]

Remove the recalibration function from the predictor:

Wolfram Language code: p2 = Predict[p, RecalibrationFunction -> None]

Visualize the new comparison plot:

Wolfram Language code: PredictorMeasurements[p2, test, "ComparisonPlot"]

Properties & Relations (2)

In ClassifierFunction, RecalibrationFunction is equivalent to renormalized probabilities:

Wolfram Language code:

ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Probabilities", RecalibrationFunction -> Sqrt]

Wolfram Language code:

Normalize[Sqrt[ClassifierFunction[Association["ExampleNumber" -> 6, "ClassNumber" -> 2, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
 ... e" -> DateObject[{2026, 2, 12, 15, 32, 
       46.896995`8.423719992106033}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Probabilities"]], Total]

In PredictorFunction, RecalibrationFunction is equivalent to TransformedDistribution action:

Wolfram Language code:

PredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 25, 
       4.411868`7.397197498244802}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Distribution", RecalibrationFunction -> (.5# + 0.1&)]

Wolfram Language code:

TransformedDistribution[.5x + 0.1, xPredictorFunction[Association["ExampleNumber" -> 51, 
  "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", 
      Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], 
       "Output" -> A ... te" -> DateObject[{2026, 2, 12, 16, 25, 
       4.411868`7.397197498244802}, "Instant", "Gregorian", 1.], "ProcessorCount" -> 4, 
    "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, 
    "Evaluations" -> {}]]][1.5, "Distribution"]]

Possible Issues (1)

Very small datasets may not allow meaningful recalibration:

Wolfram Language code: Information[Predict[{1 -> 1.3, 2 -> 2.4, 3 -> 4.4, 4 -> 5.1, 6 -> 7.3}, RecalibrationFunction -> All], "Calibrated"]

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RecalibrationFunction

Details

Examples

Basic Examples (2)

Scope (12)

Training (6)

Inference (6)

Applications (3)

MNIST (1)

Titanic (1)

Boston Homes (1)

Properties & Relations (2)

Possible Issues (1)

Text

CMS

APA

BibTeX

BibLaTeX

	None	remove existing recalibration
	f	append the function f to the existing calibrator

	None	prevent any recalibration
	Automatic	recalibrate the model when needed
	All	always recalibrate the model

RecalibrationFunction

Details

Examples

Basic Examples (2)

Scope (12)

Training (6)

Inference (6)

Applications (3)

MNIST (1)

Titanic (1)

Boston Homes (1)

Properties & Relations (2)

Possible Issues (1)

See Also

Related Guides

History

Text

CMS

APA

BibTeX

BibLaTeX