# "Multinormal"(Machine Learning Method)

• Method for LearnDistribution.
• Models the probability density using a multivariate normal (Gaussian) distribution.

# Details & Suboptions

• "Multinormal" models the probability density of a numeric space using a multivariate normal distribution as in MultinormalDistribution.
• The probability density for vector is proportional to , where and are learned parameters. If n is the size of the input numeric vector, is an n×n symmetric positive definite matrix called covariance, and is a size-n vector.
• The following options can be given:
•  "CovarianceType" "Full" type of constraint on the covariance matrix "IntrinsicDimension" Automatic effective dimensionality of the data to assume
• Possible settings for "CovarianceType" include:
•  "Diagonal" only diagonal elements are learned (the others are set to 0) "Full" all n×n elements are learned "Spherical" only diagonal elements are learned and are set to be equal
• When "CovarianceType""Full" and "IntrinsicDimension"k, with k<n, a linear dimensionality reduction is performed on the data. A full k×k covariance matrix is used to model data in the reduced space (which can be interpreted as the "signal" part), while a spherical covariance matrix is used to model the n-k remaining dimensions (which can be interpreted as the "noise" part).
• The value of "IntrinsicDimension" is ignored when "CovarianceType""Diagonal" or "CovarianceType""Spherical".
• Information[LearnedDistribution[],"MethodOption"] can be used to extract the values of options chosen by the automation system.
• LearnDistribution[,FeatureExtractor"Minimal"] can be used to remove most preprocessing and directly access the method.

# Examples

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## Basic Examples(3)

Train a "Multinormal" distribution on a numeric dataset:

 In:= Out= Look at the distribution Information:

 In:= Out= Obtain options information:

 In:= Out= Obtain an option value directly:

 In:= Out= Compute the probability density for a new example:

 In:= Out= Plot the PDF along with the training data:

 In:= Out= Generate and visualize new samples:

 In:= Out= Train a "Multinormal" distribution on a two-dimensional dataset:

 In:= In:= Out= Plot the PDF along with the training data:

 In:= Out= Use SynthesizeMissingValues to impute missing values using the learned distribution:

 In:= Out= In:= Out= Train a "Multinormal" distribution on a nominal dataset:

 In:= Out= Because of the necessary preprocessing, the PDF computation is not exact:

 In:= Out= In:= Out= Use ComputeUncertainty to obtain the uncertainty on the result:

 In:= Out= Increase MaxIterations to improve the estimation precision:

 In:= Out= 