"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 - Possible settings for "IntrinsicDimension" include:
-
Automatic try several possible dimensions "Heuristic" use a heuristic based on the data k use the specified dimension - 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
open allclose allBasic Examples (3)
Train a "Multinormal" distribution on a numeric dataset:
Look at the distribution Information:
Obtain an option value directly:
Compute the probability density for a new example:
Plot the PDF along with the training data:
Generate and visualize new samples:
Train a "Multinormal" distribution on a two-dimensional dataset:
Plot the PDF along with the training data:
Use SynthesizeMissingValues to impute missing values using the learned distribution:
Train a "Multinormal" distribution on a nominal dataset:
Because of the necessary preprocessing, the PDF computation is not exact:
Use ComputeUncertainty to obtain the uncertainty on the result:
Increase MaxIterations to improve the estimation precision: