Exponential family distributions
GPTKB entity
Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Statistical distribution family
|
| gptkbp:characterizedBy |
Log-partition function
Natural parameter Sufficient statistic |
| gptkbp:definedIn |
Probability density function of the form f(x|θ) = h(x) exp(η(θ)·T(x) - A(θ))
|
| gptkbp:hasProperty |
Exponential family form is preserved under conditioning
Exponential family form is preserved under product of distributions Closure under conditioning Closure under marginalization Closure under sampling Conjugate prior exists Convexity of log-partition function Cumulant generating function exists Dual parameterization Duality between natural and mean parameters Exponential tilting Factorization theorem applies Fisher information matrix is well-defined Identifiability Maximum entropy property Minimality Moment generating function exists Regularity Steepness Sufficient statistics are complete Exponential family form is preserved under marginalization |
| https://www.w3.org/2000/01/rdf-schema#label |
Exponential family distributions
|
| gptkbp:includes |
gptkb:Dirichlet_distribution
gptkb:Bernoulli_distribution gptkb:Poisson_distribution gptkb:Binomial_distribution gptkb:Exponential_distribution gptkb:Multinomial_distribution gptkb:Beta_distribution gptkb:Gamma_distribution gptkb:Normal_distribution |
| gptkbp:parameter |
Natural parameter
Mean parameter |
| gptkbp:relatedTo |
gptkb:Kullback-Leibler_divergence
Entropy Information geometry Maximum likelihood estimation Sufficient statistics |
| gptkbp:studiedBy |
Statistics
Machine learning |
| gptkbp:usedIn |
gptkb:Generalized_linear_models
gptkb:Variational_inference Bayesian statistics |
| gptkbp:bfsParent |
gptkb:Beta_distribution
|
| gptkbp:bfsLayer |
6
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