--- title: "PredictorFunction" language: "en" type: "Symbol" summary: "PredictorFunction[...] represents a function generated by Predict that predicts numerical values from data." keywords: - Predictor Function - Prediction Function - Predict - Prediction - Regression - Statistical Machine Learning - Machine Learning canonical_url: "https://reference.wolfram.com/language/ref/PredictorFunction.html" source: "Wolfram Language Documentation" related_guides: - title: "Supervised Machine Learning" link: "https://reference.wolfram.com/language/guide/SupervisedMachineLearning.en.md" - title: "Scientific Models" link: "https://reference.wolfram.com/language/guide/ScientificModels.en.md" - title: "Nonparametric Statistical Distributions" link: "https://reference.wolfram.com/language/guide/NonparametricStatisticalDistributions.en.md" related_functions: - title: "Predict" link: "https://reference.wolfram.com/language/ref/Predict.en.md" - title: "PredictorMeasurements" link: "https://reference.wolfram.com/language/ref/PredictorMeasurements.en.md" - title: "Information" link: "https://reference.wolfram.com/language/ref/Information.en.md" - title: "SequencePredictorFunction" link: "https://reference.wolfram.com/language/ref/SequencePredictorFunction.en.md" - title: "ClassifierFunction" link: "https://reference.wolfram.com/language/ref/ClassifierFunction.en.md" - title: "NearestFunction" link: "https://reference.wolfram.com/language/ref/NearestFunction.en.md" - title: "DimensionReducerFunction" link: "https://reference.wolfram.com/language/ref/DimensionReducerFunction.en.md" - title: "BayesianMinimizationObject" link: "https://reference.wolfram.com/language/ref/BayesianMinimizationObject.en.md" --- # PredictorFunction PredictorFunction[…] represents a function generated by Predict that predicts numerical values from data. ## Details and Options * ``PredictorFunction`` works like ``Function``. * ``PredictorFunction[…][data]`` attempts to predict the value associated with ``data``. * ``PredictorFunction[…][{data1, data2, …}]`` attempts to predict all the ``datai``. * ``PredictorFunction[…][data, prop]`` gives the specified property of the prediction associated with ``data``. * Possible properties applicable to all methods include: | | | | -------------- | ---------------------------------------------------------------------- | | "Decision" | best prediction according to the distribution and the utility function | | "Distribution" | distribution of value conditioned on input | | "SHAPValues" | Shapley additive feature explanations for each example | | "Properties" | list of all properties available | * ``"SHAPValues"`` assesses the contribution of features by comparing predictions with different sets of features removed and then synthesized. The option ``MissingValueSynthesis`` can be used to specify how the missing features are synthesized. SHAP explanations are given as deviation from the training output mean. ``"SHAPValues" -> n`` can be used to control the number of samples used for the numeric estimations of SHAP explanations. * ``PredictorFunction[…][data, …, opts]`` specifies that the predictor should use the options ``opts`` when applied to ``data``. * Possible options are: | | | | | ----------------------- | --------- | ------------------------------------------------------------- | | IndeterminateThreshold | Automatic | below what probability density to return Indeterminate | | PerformanceGoal | Automatic | which aspect of performance to optimize | | MissingValueSynthesis | Automatic | how to synthesize missing values | | RecalibrationFunction | Automatic | how to post-process predicted value | | TargetDevice | "CPU" | the target device on which to perform training | | UtilityFunction | Automatic | utility expressed as a function of actual and predicted value | * A ``PredictorFunction[…]`` trained in an older version of the Wolfram Language will still work in the current version. * ``Predict[FittedModel[…]]`` can be used to convert a fitted model into a ``PredictorFunction[…]``. * ``Predict[PredictorFunction[…], opts]`` can be used to update the values of ``PerformanceGoal``, ``IndeterminateThreshold``, ``UtilityFunction`` or ``FeatureExtractor`` of the classifier. * In ``Predict[PredictorFunction[…], FeatureExtractor -> fe]``, the ``FeatureExtractorFunction[…]`` ``fe`` will be prepended to the existing feature extractor. * ``Information[PredictorFunction[…]]`` generates an information panel about the classifier and its estimated performances. * ``Information[PredictorFunction[…], prop]`` can be used to obtain specific properties. * ``Information`` of a ``PredictorFunction[…]`` may include the following properties: | | | | ------------------------ | ---------------------------------------------------------- | | "BatchEvaluationTime" | marginal time to predict one example when a batch is given | | "EvaluationTime" | time needed to predict one example | | "ExampleNumber" | number of training examples | | "FeatureTypes" | feature types of the predictor input | | "FunctionMemory" | memory needed to store the predictor | | "FunctionProperties" | all prediction properties available for this predictor | | "IndeterminateThreshold" | value of IndeterminateThreshold used by the predictor | | "LearningCurve" | performance as function of training set size | | "MaxTrainingMemory" | maximum memory used during training | | "MeanCrossEntropy" | estimated mean cross entropy of the predictor | | "Method" | value of Method used by the predictor | | "MethodDescription" | summary of the method | | "MethodOption" | full method option to be reused in a new training | | "MethodParameters" | parameter settings of the method | | "Properties" | all information properties available for this predictor | | "StandardDeviation" | estimated standard deviation of the predictor | | "FeatureExtractor" | feature extractor as FeatureExtractorFunction | | "TrainingLabelMean" | mean label value seen during training | | "TrainingTime" | time used by Predict to generate the predictor | | "UtilityFunction" | value of UtilityFunction used by the predictor | * ``Information`` properties also include all method suboptions. --- ## Examples (15) ### Basic Examples (2) Train a ``PredictorFunction`` : ```wl In[1]:= trainingData = {1.1 -> 1, 2.2 -> 2.5, 3.3 -> 3, 4.2 -> 5.8, 6.7 -> 9.8}; p = Predict[trainingData] Out[1]= PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... " -> DateObject[{2018, 11, 29, 15, 22, 2.912121`7.216784404770749}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Use the trained ``PredictorFunction`` to predict an output, given some feature: ```wl In[2]:= p[1.4] Out[2]= 1.10459 ``` Predict multiple examples: ```wl In[3]:= p[{3.4, 6.6, 8.2}] Out[3]= {4.2566, 9.29981, 11.8214} ``` Calculate the probability distribution of the predicted value: ```wl In[4]:= Plot[PDF[p[1.4, "Distribution"], x], {x, -5, 5}, PlotRange -> All, Frame -> True] Out[4]= [image] ``` --- Generate a ``PredictorFunction`` using multiple features: ```wl In[1]:= p = Predict[{ {1.5, 2.2} -> 1.2, {3.2, 3.5} -> 2.7, {5.3, 19.1} -> 4.2, {7.7, 20.3} -> 5.5}] Out[1]= PredictorFunction[Association["ExampleNumber" -> 4, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "NumericalVector", "Lengt ... "Date" -> DateObject[{2018, 11, 29, 15, 22, 9.60375`7.735015832901325}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Use the function on a new example: ```wl In[2]:= p[{1.5, 2.2}] Out[2]= 2.58093 ``` Predict an example that has missing features: ```wl In[3]:= p[{5.6, Missing[]}] Out[3]= 3.7522 ``` Obtain general information about the predictor: ```wl In[4]:= Information[p] Out[4]= | | | :------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | "Predictor information" | | \| \| \| \| ------------------ ... \| \| "Training time" \| Quantity[833., "Milliseconds"] \| | ``` ### Scope (6) Train a ``PredictorFunction`` on textual data: ```wl In[1]:= p = Predict[{"this is large" -> 7., "this is small" -> -5., "this is tiny and small" -> -10, "this is medium or large" -> 4., "this is large and big" -> 15., "this is small and little" -> -8.}] Out[1]= PredictorFunction[…] ``` Predict the values of new examples: ```wl In[2]:= p[{"How large is it?", "Is it small or medium?"}] Out[2]= {7., 4.} ``` --- Train a ``PredictorFunction`` to recognize the frequency of ``SawtoothWave`` sounds: ```wl In[1]:= p = Predict[{Sound[SampledSoundFunction[Function[{Play`Time39}, Block[{t = 0. + 0.000125*Play`Time39}, (SawtoothWave[324.45795035524935*t] - 0.5001160510727303)*2.0031463158766147]], 2400, 8000]] -> 324, Sound[SampledSoundFunction[Function[{Play`Time40}, Block[{t = 0. + 0.000125*Play`Time40}, (SawtoothWave[226.36058426333676*t] - 0.5010053417184481)*2.0069343605226013]], 2400, 8000]] -> 226, Sound[SampledSoundFunction[Function[{Play`Time41}, Block[{t = 0. + 0.000125*Play`Time41}, (SawtoothWave[315.7789342382401*t] - 0.5049934194652432)*2.020583866475329]], 2400, 8000]] -> 316, Sound[SampledSoundFunction[Function[{Play`Time42}, Block[{t = 0. + 0.000125*Play`Time42}, (SawtoothWave[327.59406235471874*t] - 0.49904376688894914)*2.0074978690687044]], 2400, 8000]] -> 328, Sound[SampledSoundFunction[Function[{Play`Time52}, Block[{t = 0. + 0.000125*Play`Time52}, (SawtoothWave[273.0283558209228*t] - 0.4999736167215616)*2.0066458385060892]], 2400, 8000]] -> 273}] Out[1]= PredictorFunction[…] ``` Predict the values of new examples: ```wl In[2]:= test = {Sound[SampledSoundFunction[Function[{Play`Time56}, Block[{t = 0. + 0.000125*Play`Time56}, (SawtoothWave[244.15080360431867*t] - 0.500059985761311)*2.0041296772661803]], 2400, 8000]] -> 244, Sound[SampledSoundFunction[Function[{Play`Time62}, Block[{t = 0. + 0.000125*Play`Time62}, (SawtoothWave[291.9708009764995*t] - 0.5036494453307649)*2.014705247404505]], 2400, 8000]] -> 292}; In[3]:= p[test[[All, 1]]] Out[3]= {300.5, 300.5} ``` --- Train a ``PredictorFunction`` : ```wl In[1]:= p = Predict[{1.2, 2, 3.5, 4, 5.2} -> {2.3, 1.2, 5.5, 7.7, 9.9}] Out[1]= PredictorFunction[…] ``` Generate a ``PredictorMeasurementsObject`` of the function applied to a test set: ```wl In[2]:= pm = PredictorMeasurements[p, {1.4 -> 2.5, 4.5 -> 8.6, 5.4 -> 10.2, 3.3 -> 3}] Out[2]= PredictorMeasurementsObject[…] ``` Get the standard deviation of the residuals of the function on the test set: ```wl In[3]:= pm["StandardDeviation"] Out[3]= 0.926495 ``` Visualize the scatter plot of the test values as a function of the predicted values: ```wl In[4]:= pm["ComparisonPlot"] Out[4]= [image] ``` --- Generate a predictor function whose input is an association: ```wl In[1]:= p = Predict[{ <|"variable1" -> 1.2, "variable2" -> 3.1|> -> 0.3, <|"variable1" -> 6.8, "variable2" -> 5.8|> -> 2.3, <|"variable1" -> 8.3|> -> 4.1}] Out[1]= PredictorFunction[…] ``` Use the function on an example: ```wl In[2]:= p[<|"variable1" -> 4.5, "variable2" -> 5.5|>] Out[2]= 2.23333 ``` Predict examples containing missing features: ```wl In[3]:= p[{<|"variable1" -> 3.1|>, <|"variable2" -> 4.6|>, <||>}] Out[3]= {2.23333, 2.80626, 2.25835} ``` --- Construct a ``Dataset`` with a list of associations: ```wl In[1]:= d = Dataset[{<|"age" -> 32, "height" -> 160, "gender" -> "female"|>, <|"height" -> 183, "age" -> 41, "gender" -> "female"|>, <|"height" -> 123, "age" -> 30, "gender" -> "female"|>, <|"height" -> 175, "age" -> 21, "gender" -> "male"|>, <|"height" -> 150, "age" -> 11, "gender" -> "male"|>, <|"age" -> 52, "height" -> 164, "gender" -> "female"|>}] Out[1]= Dataset[<>] ``` Train a ``PredictorFunction`` to predict the feature ``"age"`` as function of the other features: ```wl In[2]:= p = Predict[d -> "age"] Out[2]= PredictorFunction[…] ``` Once the ``PredictorFunction`` is trained, any input format can be used. Predict an example formatted as an association: ```wl In[3]:= p[<|"height" -> 120, "gender" -> "female"|>] Out[3]= 29.3218 ``` Find out the order of the features, and classify an example formatted as a list: ```wl In[4]:= Information[p, FeatureNames] Out[4]= {"height", "gender"} In[5]:= p[{120, "female"}] Out[5]= 29.3218 ``` Classify examples in a ``Dataset`` : ```wl In[6]:= dnew = Dataset[{<|"height" -> 120, "gender" -> "female"|>, <|"height" -> 150, "gender" -> "male"|>, <|"height" -> 80, "gender" -> "female"|>}] Out[6]= Dataset[<>] In[7]:= p[dnew] Out[7]= {29.3218, 12.8573, 19.265} ``` --- Load a dataset of wine quality as a function of the wines' physical properties: ```wl In[1]:= wine = ResourceData["Sample Data: Wine Quality"]; ``` Train a predictor to estimate wine quality: ```wl In[2]:= p = Predict[wine -> "WineQuality"] x = KeyDrop[wine, "WineQuality"]; Out[2]= PredictorFunction[«1»] ``` Examine an example bottle: ```wl In[3]:= bottle = Last[x] Out[3]= Dataset[Association["FixedAcidity" -> 6., "VolatileAcidity" -> 0.21, "CitricAcid" -> 0.38, "ResidualSugar" -> 0.8, "Chlorides" -> 0.02, "FreeSulfurDioxide" -> 22., "TotalSulfurDioxide" -> 98., "Density" -> 0.98941, "PH" -> 3.26, "Sulphates" -> 0.32, "Alcohol" -> 11.8]] ``` Predict the example bottle's quality: ```wl In[4]:= predictedquality = p[bottle] Out[4]= 6.09044 ``` Calculate how much higher or lower this bottle's predicted quality is than the mean: ```wl In[5]:= meanquality = Information[p, "TrainingLabelMean"]; predictedquality - meanquality Out[5]= 0.212532 ``` Get an estimation for how much each feature impacted the predictor's output for this bottle: ```wl In[6]:= impacts = p[bottle, "SHAPValues"] Out[6]= <|"FixedAcidity" -> 0.0372977, "VolatileAcidity" -> -0.0115963, "CitricAcid" -> 0.0337296, "ResidualSugar" -> -0.207066, "Chlorides" -> 0.0929426, "FreeSulfurDioxide" -> 0.108215, "TotalSulfurDioxide" -> 0.0501292, "Density" -> 0.0744508, "PH" -> 0.0327222, "Sulphates" -> -0.0379025, "Alcohol" -> 0.0396088|> ``` Visualize these feature impacts: ```wl In[7]:= BarChart[Sort[impacts], ChartLabels -> Placed[Automatic, After], ImageSize -> Medium, BarOrigin -> Left, PlotLabel -> "Impact of Feature on Prediction"] Out[7]= [image] ``` Confirm that the Shapley values fully explain the predicted quality: ```wl In[8]:= Total[impacts] meanquality + Total[impacts] == predictedquality Out[8]= 0.212532 Out[8]= True ``` Learn a distribution of the data that treats each feature as independent: ```wl In[9]:= dist = LearnDistribution[x, Method -> {"Multinormal", "CovarianceType" -> "Diagonal"}] Out[9]= LearnedDistribution[Association["ExampleNumber" -> 4898, "Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["FixedAcidity" -> Association["Type" -> "Numerical"], "VolatileAcidity" -> Asso ... n["Quantiles" -> CompressedData["«620»"], "LeftBoundary" -> -1.411857857101751, "LeftScale" -> 0.38626310063157926, "LeftTailNorm" -> 0.022]], "Entropy" -> Around[5.471660028467438, 0.16096729925003606], "EntropySampleSize" -> 500]] ``` Estimate SHAP value feature importance for 100 bottles of wine, using 5 samples for each estimation: ```wl In[10]:= winebottles = RandomSample[x, 100]; shaps = p[winebottles, "SHAPValues" -> 5, MissingValueSynthesis -> dist]; Out[10]= {28.7542, Null} ``` Calculate how important each feature is to the model: ```wl In[11]:= importance = Mean[Abs[shaps]] Out[11]= <|"FixedAcidity" -> 0.0402703, "VolatileAcidity" -> 0.124879, "CitricAcid" -> 0.0549411, "ResidualSugar" -> 0.0675542, "Chlorides" -> 0.0801382, "FreeSulfurDioxide" -> 0.0849935, "TotalSulfurDioxide" -> 0.0604899, "Density" -> 0.0853172, "PH" -> 0.051762, "Sulphates" -> 0.0377501, "Alcohol" -> 0.288131|> ``` Visualize the model's feature importance: ```wl In[12]:= BarChart[Sort[importance], ChartLabels -> Placed[Automatic, After], ImageSize -> Medium, BarOrigin -> Left, PlotLabel -> "Average Feature Impact"] Out[12]= [image] ``` Visualize a nonlinear relationship between a feature's value and its impact on the model's prediction: ```wl In[13]:= ListPlot[Thread[{Normal[winebottles][[All, "TotalSulfurDioxide"]], shaps[[All, "TotalSulfurDioxide"]]}], AxesLabel -> {"Feature Value", "Feature Impact"}, PlotMarkers -> Automatic] Out[13]= [image] ``` ### Options (7) #### IndeterminateThreshold (1) Train a ``PredictorFunction`` : ```wl In[1]:= p = Predict[{1 -> 0.3, 2 -> 1.4, 3 -> 4.5, 4 -> 6.8}] Out[1]= PredictorFunction[Association["ExampleNumber" -> 4, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... " -> DateObject[{2018, 11, 29, 15, 22, 36.946019`8.32014262858112}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Visualize the probability density for a given example: ```wl In[2]:= example = 2.2; pdf = PDF[p[example, "Distribution"]] Out[2]= Function[\[FormalX], 0.651111 E^-1.33187 (-2.58099 + \[FormalX])^2] In[3]:= Plot[pdf[x], {x, 0, 6}, PlotRange -> All] Out[3]= [image] ``` The value with the highest probability density is predicted: ```wl In[4]:= p[example] Out[4]= 2.58099 ``` No prediction is made if the maximum probability density is below a specified threshold: ```wl In[5]:= p[example, IndeterminateThreshold -> 0.7] Out[5]= Indeterminate ``` Update the value of the threshold permanently: ```wl In[6]:= p2 = Predict[p, IndeterminateThreshold -> 0.7] Out[6]= PredictorFunction[Association["ExampleNumber" -> 4, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... " -> DateObject[{2018, 11, 29, 15, 22, 36.946019`8.32014262858112}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] In[7]:= p2[example] Out[7]= Indeterminate ``` #### MissingValueSynthesis (1) Train a predictor with two input features: ```wl In[1]:= x = {{1, 3}, {2, 4}, {3, 5}, {4, 4}, {5, 8}, {6, 9}, {7, 4}, {8, 6}, {9, 12}}; y = {2, 4, 5, 4, 6, 7, 4, 5, 9}; p = Predict[x -> y] Out[1]= PredictorFunction[Association["ExampleNumber" -> 9, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"], "f2" -> Assoc ... "Date" -> DateObject[{2021, 4, 9, 18, 22, 24.415184`8.140234984217171}, "Instant", "Gregorian", -4.], "ProcessorCount" -> 6, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Get the prediction for an example that has a missing value: ```wl In[2]:= p[{5, Missing[]}] Out[2]= 5.10907 ``` Set the missing value synthesis to replace missing variables with their most likely value given known values (which is the default behavior): ```wl In[3]:= p[{5, Missing[]}, MissingValueSynthesis -> "ModeFinding"] Out[3]= 5.10907 ``` Replace missing variables with random samples conditioned on known values: ```wl In[4]:= p[{5, Missing[]}, MissingValueSynthesis -> "RandomSampling"] Out[4]= 3.70258 ``` Averaging over many random imputations is usually the best strategy and allows obtaining the uncertainty caused by the imputation: ```wl In[5]:= MeanAround[Table[p[{5, Missing[]}, MissingValueSynthesis -> "RandomSampling"], 100]] Out[5]= Around[5.009737917054653, 0.1275219937576369] ``` Specify a learning method during training to control how the distribution of data is learned: ```wl In[6]:= p = Predict[x -> y, MissingValueSynthesis -> "KernelDensityEstimation"] Out[6]= PredictorFunction[Association["ExampleNumber" -> 9, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"], "f2" -> Assoc ... "Date" -> DateObject[{2021, 4, 9, 18, 23, 57.39158`8.511423154725838}, "Instant", "Gregorian", -4.], "ProcessorCount" -> 6, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Predict an example with missing values using the ``"KernelDensityEstimation"`` distribution to condition values: ```wl In[7]:= p[{5, Missing[]}] Out[7]= 4.61036 ``` Provide an existing ``LearnedDistribution`` at training to use it when imputing missing values during training and later evaluations: ```wl In[8]:= dist = LearnDistribution[x, Method -> "Multinormal"]; p = Predict[x -> y, MissingValueSynthesis -> dist] p[{5, Missing[]}] Out[8]= PredictorFunction[Association["ExampleNumber" -> 9, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"], "f2" -> Assoc ... "Date" -> DateObject[{2021, 4, 9, 18, 24, 46.087906`8.41616195305408}, "Instant", "Gregorian", -4.], "ProcessorCount" -> 6, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] Out[8]= 5.10798 ``` Specify an existing ``LearnedDistribution`` to synthesize missing values for an individual evaluation: ```wl In[9]:= dist2 = LearnDistribution[x, Method -> "KernelDensityEstimation"]; p[{5, Missing[]}, MissingValueSynthesis -> dist2] Out[9]= 4.58529 ``` Control both the learning method and the evaluation strategy by passing an association at training: ```wl In[10]:= p = Predict[x -> y, MissingValueSynthesis -> <|"LearningMethod" -> "Multinormal", "EvaluationStrategy" -> "RandomSampling"|>]; p[{5, Missing[]}] Out[10]= 3.24898 ``` #### RecalibrationFunction (2) Train a predictor: ```wl In[1]:= p = Predict[{1 -> 1.3, 2 -> 2.4, 3 -> 4.4, 4 -> 5.1, 6 -> 7.3}] Out[1]= PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... "Date" -> DateObject[{2021, 4, 2, 12, 7, 54.066566`8.4855037609736}, "Instant", "Gregorian", 2.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Compute the prediction: ```wl In[2]:= p[3.4] Out[2]= 4.4 ``` Compute the predictive distribution: ```wl In[3]:= p[3.4, "Distribution"] Out[3]= NormalDistribution[4.4, 1.28374] ``` Temporarily set a recalibration function to apply to the prediction: ```wl In[4]:= p[3.4, RecalibrationFunction -> (.5# + 0.1&)] Out[4]= 2.3 ``` Compute the predictive distribution with this new recalibration: ```wl In[5]:= p[3.4, "Distribution", RecalibrationFunction -> (.5# + 0.1&)] Out[5]= NormalDistribution[2.3, 0.641872] ``` --- Load the Boston Homes dataset: ```wl In[1]:= training = RandomSample[ResourceData["Sample Data: Boston Homes", "TrainingData"]]; test = ResourceData["Sample Data: Boston Homes", "TestData"]; ``` Train a predictor with model calibration: ```wl In[2]:= p = Predict[training, Method -> "RandomForest", RecalibrationFunction -> All] Out[2]= PredictorFunction[«1»] ``` Visualize the comparison plot on a test set: ```wl In[3]:= PredictorMeasurements[p, test, "ComparisonPlot"] Out[3]= [image] ``` Remove the recalibration function from the predictor: ```wl In[4]:= p2 = Predict[p, RecalibrationFunction -> None] Out[4]= PredictorFunction[«1»] ``` Visualize the new comparison plot: ```wl In[5]:= PredictorMeasurements[p2, test, "ComparisonPlot"] Out[5]= [image] ``` #### TargetDevice (1) Train a predictor using a neural network: ```wl In[1]:= trainingData = RandomReal[1, {2000, 4}] -> RandomReal[1, 2000]; predictor = Predict[trainingData, Method -> "NeuralNetwork", TargetDevice -> "GPU"] ``` Evaluate the resulting predictor on system's default GPU and look at its ``AbsoluteTiming`` : ```wl In[2]:= n = 10000 AbsoluteTiming[predictor[RandomReal[1, {n, 4}], TargetDevice -> "GPU"];] ``` Compare the previous timing with the one achieved by using the default CPU computation: ```wl In[3]:= AbsoluteTiming[predictor[RandomReal[1, {n, 4}]];] ``` #### UtilityFunction (1) Train a predictor function: ```wl In[1]:= trainingset = {1 -> 1.1, 2 -> 5.5, 3 -> 6.1, 4 -> 7.7, 5 -> 9.2}; In[2]:= p = Predict[trainingset] Out[2]= PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... -> DateObject[{2018, 11, 29, 15, 23, 31.487384`8.250711561266273}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] ``` Visualize the probability density for a given example: ```wl In[3]:= example = 2.6; pdf = PDF[p[example, "Distribution"]] Out[3]= Function[\[FormalX], 0.370489 E^-0.431222 (-5.19097 + \[FormalX])^2] In[4]:= Plot[pdf[x], {x, 1, 12}, PlotRange -> All] Out[4]= [image] ``` By default, the value with the highest probability density is predicted: ```wl In[5]:= p[example] Out[5]= 5.19097 ``` Define a utility function that penalizes the predicted value's being smaller than the actual value: ```wl In[6]:= utility[a_, p_] := -Piecewise[{{Exp[p - a], a < p}, {Exp[2 * (a - p)], a ≥ p}}] ``` Plot this function for a given actual value: ```wl In[7]:= Plot[utility[0, p], {p, -1, 2}] Out[7]= [image] ``` The predictor decision is now changed despite the probability density's being unchanged: ```wl In[8]:= p[example, UtilityFunction -> utility] Out[8]= 5.99991 ``` Update the value of the utility function permanently: ```wl In[9]:= p2 = Predict[p, UtilityFunction -> utility] Out[9]= PredictorFunction[Association["ExampleNumber" -> 5, "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Input" -> Association["f1" -> Association["Type" -> "Numerical"]], "Output" -> As ... -> DateObject[{2018, 11, 29, 15, 23, 31.487384`8.250711561266273}, "Instant", "Gregorian", -8.], "ProcessorCount" -> 4, "ProcessorType" -> "x86-64", "OperatingSystem" -> "MacOSX", "SystemWordLength" -> 64, "Evaluations" -> {}]]] In[10]:= p2[example] Out[10]= 5.91158 ``` #### PerformanceGoal (1) Obtain the built-in ``PredictorFunction`` ``"NameAge"`` : ```wl In[1]:= p = Predict["NameAge"] Out[1]= PredictorFunction[Association[ "Input" -> Association["Preprocessor" -> MachineLearning`MLProcessor["ToMLDataset", Association["Output" -> Association["FirstName" -> Association["Type" -> "Text", "Weights" -> 1]], "Preprocessor ... hod" -> "NameAge", "Processor" -> MachineLearning`PackageScope`Preprocessor["Identity"]], "ExampleNumber" -> Missing[], "Prior" -> Automatic, "Utility" -> (DiracDelta[#2 - #1] & ), "Threshold" -> 0.015, "PerformanceGoal" -> Automatic]] ``` Set a custom utility function to use with this predictor: ```wl In[2]:= utility[a_, p_] := -Piecewise[{{Exp[p - a], a < p}, {Exp[3 * (a - p)], a ≥ p}}] ``` Compute the time required to use an example with this utility function: ```wl In[3]:= AbsoluteTiming[p["Bob", UtilityFunction -> utility]] Out[3]= {2.36019, 74.5149} ``` Use ``PerformanceGoal`` to use a faster but less accurate result: ```wl In[4]:= AbsoluteTiming[p["Bob", UtilityFunction -> utility, PerformanceGoal -> "Speed"]] Out[4]= {0.071446, 73.1318} ``` ## See Also * [`Predict`](https://reference.wolfram.com/language/ref/Predict.en.md) * [`PredictorMeasurements`](https://reference.wolfram.com/language/ref/PredictorMeasurements.en.md) * [`Information`](https://reference.wolfram.com/language/ref/Information.en.md) * [`SequencePredictorFunction`](https://reference.wolfram.com/language/ref/SequencePredictorFunction.en.md) * [`ClassifierFunction`](https://reference.wolfram.com/language/ref/ClassifierFunction.en.md) * [`NearestFunction`](https://reference.wolfram.com/language/ref/NearestFunction.en.md) * [`DimensionReducerFunction`](https://reference.wolfram.com/language/ref/DimensionReducerFunction.en.md) * [`BayesianMinimizationObject`](https://reference.wolfram.com/language/ref/BayesianMinimizationObject.en.md) ## Related Guides * [Supervised Machine Learning](https://reference.wolfram.com/language/guide/SupervisedMachineLearning.en.md) * [Scientific Models](https://reference.wolfram.com/language/guide/ScientificModels.en.md) * [Nonparametric Statistical Distributions](https://reference.wolfram.com/language/guide/NonparametricStatisticalDistributions.en.md) ## History * [Introduced in 2014 (10.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn100.en.md) \| [Updated in 2018 (11.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn113.en.md) ▪ [2019 (12.0)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn120.en.md) ▪ [2021 (12.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn123.en.md)