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LearnedDistribution
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LearnedDistribution

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represents a distribution generated by LearnDistribution.

Details and Options

  • The following functions can be used on a LearnedDistribution[…]:
  • PDF[dist,…]probability or probability density for data
    RandomVariate[dist]random samples generated from the distribution
    SynthesizeMissingValues[dist,…]fill in missing values according to the distribution
    RarerProbability[dist,…]compute the probability to generate a sample with lower PDF than a given example
  • When acting on a LearnedDistribution[…], the functions PDF and RarerProbability can be used with the following options:
  • PerformanceGoal Automaticaspect of performance to optimize
    MaxIterations Automaticnumber of iterations to use when a Monte Carlo integration is performed
    ComputeUncertainty Falsewhether to return probabilities with their uncertainty
  • Possible settings for PerformanceGoal include:
  • "Quality"maximize the quality of the result
    "Speed"maximize the speed of the result
    Automaticautomatic tradeoff between speed and quality
  • Information[LearnedDistribution[…]] generates an information panel about the distribution and its estimated performances.
  • Information[LearnedDistribution[…],prop] can be used to obtain specific properties.
  • Information of a LearnedDistribution may include the following properties:
  • "BatchPDFTime"marginal time to appy PDF to one example when a batch is given
    "BatchSamplingTime"marginal time to generate one example in a batch
    "Entropy"estimated entropy of the distribution
    "ExampleNumber"number of training examples
    "FeatureTypes"types of the distribution variables
    "FunctionMemory"memory needed to store the distribution
    "LearningCurve"performance as a function of the training set size
    "MaxTrainingMemory"maximum memory used during training
    "Method"value of Method used by LearnDistribution
    "MethodDescription"summary of the method
    "MethodOption"full method option to be reused in a new training
    "PDFTime"time to apply PDF to a unique example
    "Properties"all information properties available for this distribution
    "SamplingTime"time to sample one example
    "TrainingTime"time used by LearnDistribution to generate the distribution
  • Information properties also include all method suboptions.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Train a LearnedDistribution[…] on a numeric dataset:

In[1]:=1
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https://wolfram.com/xid/0fq8cwmlehkl2-5hhlm7
Out[1]=1

Look at the distribution Information:

In[2]:=2
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https://wolfram.com/xid/0fq8cwmlehkl2-zci6sv
Out[2]=2

Obtain available information properties:

In[3]:=3
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https://wolfram.com/xid/0fq8cwmlehkl2-d28lne
Out[3]=3

Generate a new example based on the learned distribution:

In[4]:=4
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https://wolfram.com/xid/0fq8cwmlehkl2-38oizs
Out[4]=4

Compute the PDF of a new example:

In[5]:=5
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https://wolfram.com/xid/0fq8cwmlehkl2-ed58y3
Out[5]=5

Train a LearnedDistribution[…] on a nominal dataset:

In[1]:=1
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https://wolfram.com/xid/0fq8cwmlehkl2-1giaj9
Out[1]=1

Generate a new example based on the learned distribution:

In[2]:=2
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https://wolfram.com/xid/0fq8cwmlehkl2-67g5d3
Out[2]=2

Compute the probability of the examples "A" and "B":

In[3]:=3
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https://wolfram.com/xid/0fq8cwmlehkl2-wmcrl5
Out[3]=3

Train a LearnedDistribution[…] on a two-dimensional dataset:

In[1]:=1
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https://wolfram.com/xid/0fq8cwmlehkl2-9eb8g
Out[1]=1

Generate a new example based on the learned distribution:

In[2]:=2
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https://wolfram.com/xid/0fq8cwmlehkl2-mxqvzs
Out[2]=2

Compute the probability of two examples:

In[3]:=3
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https://wolfram.com/xid/0fq8cwmlehkl2-q48rx3
Out[3]=3

Impute the missing value of an example:

In[4]:=4
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https://wolfram.com/xid/0fq8cwmlehkl2-u4nvqc
Out[4]=4

Options  (3)Common values & functionality for each option

ComputeUncertainty  (1)

Train a "Multinormal" distribution on a nominal dataset:

In[1]:=1
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https://wolfram.com/xid/0fq8cwmlehkl2-36gxxt
Out[1]=1

A stochastic preprocessing is needed to transform the nominal variables into numeric variables; the PDF computation is approximate:

In[2]:=2
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https://wolfram.com/xid/0fq8cwmlehkl2-wbm3in
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fq8cwmlehkl2-jokluj
Out[3]=3

Use ComputeUncertainty to obtain the uncertainty on the result:

In[4]:=4
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https://wolfram.com/xid/0fq8cwmlehkl2-29ml4l
Out[4]=4

Increase MaxIterations to improve the estimation precision:

In[5]:=5
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https://wolfram.com/xid/0fq8cwmlehkl2-5lufi6
Out[5]=5

MaxIterations  (1)

Train a "Multinormal" distribution on a nominal dataset:

In[8]:=8
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https://wolfram.com/xid/0fq8cwmlehkl2-7hof4x
Out[8]=8

A stochastic preprocessing is needed to transform the nominal variables into numeric variables; the PDF computation is approximate:

In[9]:=9
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https://wolfram.com/xid/0fq8cwmlehkl2-1j1a3u
Out[9]=9

Increase MaxIterations to improve the estimation precision:

In[10]:=10
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https://wolfram.com/xid/0fq8cwmlehkl2-6ns5om
Out[10]=10

PerformanceGoal  (1)

Train a "Multinormal" distribution on a nominal dataset:

In[2]:=2
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https://wolfram.com/xid/0fq8cwmlehkl2-dcdzb2
Out[2]=2

A stochastic preprocessing is needed to transform the nominal variables into numeric variables; the PDF computation is approximate:

In[6]:=6
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https://wolfram.com/xid/0fq8cwmlehkl2-labfq3
Out[6]=6

Use PerformanceGoal"Quality" to improve the estimation precision:

In[9]:=9
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https://wolfram.com/xid/0fq8cwmlehkl2-10ez16
Out[9]=9

Compare with PerformanceGoal"Speed":

In[10]:=10
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https://wolfram.com/xid/0fq8cwmlehkl2-pv1e0d
Out[10]=10
Wolfram Research (2019), LearnedDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/LearnedDistribution.html.
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Wolfram Research (2019), LearnedDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/LearnedDistribution.html.

Text

Wolfram Research (2019), LearnedDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/LearnedDistribution.html.

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Wolfram Research (2019), LearnedDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/LearnedDistribution.html.

CMS

Wolfram Language. 2019. "LearnedDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LearnedDistribution.html.

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Wolfram Language. 2019. "LearnedDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LearnedDistribution.html.

APA

Wolfram Language. (2019). LearnedDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LearnedDistribution.html

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Wolfram Language. (2019). LearnedDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LearnedDistribution.html

BibTeX

@misc{reference.wolfram_2025_learneddistribution, author="Wolfram Research", title="{LearnedDistribution}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/LearnedDistribution.html}", note=[Accessed: 12-May-2025 ]}

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@misc{reference.wolfram_2025_learneddistribution, author="Wolfram Research", title="{LearnedDistribution}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/LearnedDistribution.html}", note=[Accessed: 12-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_learneddistribution, organization={Wolfram Research}, title={LearnedDistribution}, year={2019}, url={https://reference.wolfram.com/language/ref/LearnedDistribution.html}, note=[Accessed: 12-May-2025 ]}

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@online{reference.wolfram_2025_learneddistribution, organization={Wolfram Research}, title={LearnedDistribution}, year={2019}, url={https://reference.wolfram.com/language/ref/LearnedDistribution.html}, note=[Accessed: 12-May-2025 ]}