multivariate Gaussian distribution

URI: https://gptkb.org/entity/multivariate_Gaussian_distribution

GPTKB entity

Statements (52)

Predicate	Object
gptkbp:instanceOf	gptkb:organization
gptkbp:alsoKnownAs	gptkb:multivariate_normal_distribution
gptkbp:characteristic	exp(i t^T μ - 1/2 t^T Σ t)
gptkbp:conditionalDistribution	gptkb:multivariate_normal_distribution
gptkbp:covarianceMatrixSymbol	Σ
gptkbp:cumulantGeneratingFunction	μ^T t + 1/2 t^T Σ t
gptkbp:definedIn	n-dimensional real vector space
gptkbp:densityFunctionDependsOn	covariance matrix mean vector
gptkbp:entropyFormula	(1/2) ln((2πe)^k \|Σ\|)
gptkbp:firstDescribed	gptkb:Carl_Friedrich_Gauss
gptkbp:hasDensityFunction	yes
gptkbp:hasSpecialCase	gptkb:exponential_family gptkb:elliptical_distribution
https://www.w3.org/2000/01/rdf-schema#label	multivariate Gaussian distribution
gptkbp:ifCovarianceDiagonal	independent components
gptkbp:ifCovarianceIdentity	gptkb:standard_multivariate_normal_distribution
gptkbp:ifCovarianceSingular	gptkb:degenerate_distribution
gptkbp:ifMeanZero	centered distribution
gptkbp:marginalDistribution	gptkb:univariate_normal_distribution
gptkbp:maximumEntropyDistribution	given mean and covariance
gptkbp:meanVectorSymbol	μ
gptkbp:moments	all moments exist
gptkbp:parameter	covariance matrix mean vector
gptkbp:pdfFormula	(2π)^{-k/2} \|Σ\|^{-1/2} exp(-1/2 (x-μ)^T Σ^{-1} (x-μ))
gptkbp:relatedTo	gptkb:Hotelling's_T-squared_distribution gptkb:Mahalanobis_distance gptkb:normal_distribution gptkb:Gaussian_copula gptkb:Wishart_distribution gptkb:multivariate_t-distribution gptkb:Gaussian_process Bayesian statistics linear regression covariance structure random vector
gptkbp:supports	entire n-dimensional real space
gptkbp:usedFor	gptkb:principal_component_analysis gptkb:Gaussian_processes gptkb:Gaussian_mixture_models Kalman filtering linear discriminant analysis modeling correlated variables
gptkbp:usedIn	gptkb:machine_learning gptkb:signal_processing statistics Bayesian inference pattern recognition
gptkbp:bfsParent	gptkb:multivariate_normal_distribution gptkb:Machine_Learning_by_Andrew_Ng
gptkbp:bfsLayer	6