Dirichlet distribution
E466249
conjugate prior
continuous distribution
exponential family distribution
multivariate distribution
probability distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Dirichlet distribution density | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
conjugate prior
ⓘ
continuous distribution ⓘ exponential family distribution ⓘ multivariate distribution ⓘ probability distribution ⓘ |
| appearsIn |
Bayesian text modeling
NERFINISHED
ⓘ
document clustering ⓘ ecology ⓘ genetics ⓘ |
| belongsTo | multivariate continuous distributions ⓘ |
| belongsToFamily | Dirichlet family NERFINISHED ⓘ |
| conjugateTo |
categorical distribution
ⓘ
multinomial distribution NERFINISHED ⓘ |
| definedOn | probability simplex ⓘ |
| field |
machine learning
ⓘ
probability theory ⓘ statistics ⓘ |
| generalizes | beta distribution ⓘ |
| hasDensityFunction | proportional to product of powers of components ⓘ |
| hasLimitingCase |
degenerate distribution on simplex as concentration goes to infinity
ⓘ
distribution concentrated on vertices of simplex as concentration goes to zero ⓘ |
| hasProperty |
components are nonnegative
ⓘ
components sum to 1 ⓘ exchangeable when parameters equal ⓘ mean equals normalized alpha parameters ⓘ variance decreases as concentration increases ⓘ |
| hasSpecialCase | beta distribution ⓘ |
| namedAfter | Peter Gustav Lejeune Dirichlet NERFINISHED ⓘ |
| normalizingConstant | multivariate beta function ⓘ |
| parameterizedBy |
alpha vector
ⓘ
concentration parameters ⓘ |
| parameterSpace | positive real numbers ⓘ |
| relatedTo |
Dirichlet process
NERFINISHED
ⓘ
Dirichlet-multinomial distribution NERFINISHED ⓘ |
| samplingMethod | normalized gamma variables ⓘ |
| support | k-dimensional probability simplex ⓘ |
| usedAs |
prior for categorical distribution
ⓘ
prior for multinomial distribution ⓘ |
| usedFor |
Bayesian inference for multinomial parameters
ⓘ
modeling uncertainty over discrete probability vectors ⓘ prior over mixture weights ⓘ prior over topic proportions ⓘ smoothing categorical frequency estimates ⓘ |
| usedIn |
Bayesian machine learning
NERFINISHED
ⓘ
Bayesian mixture models NERFINISHED ⓘ Bayesian nonparametrics NERFINISHED ⓘ Bayesian statistics NERFINISHED ⓘ Latent Dirichlet Allocation NERFINISHED ⓘ topic modeling ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dirichlet distribution density