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gptkbp:instanceOf
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gptkb:organization
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gptkbp:application
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genetics
natural language processing
image processing
document classification
mixture models
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gptkbp:conjugatePriorFor
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multinomial distribution
categorical distribution
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gptkbp:dimensions
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gptkb:K-1
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gptkbp:entropy
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function of alpha vector and digamma function
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gptkbp:firstDescribed
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1939
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gptkbp:generalizes
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gptkb:Beta_distribution
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gptkbp:hasSpecialCase
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gptkb:asymmetric_Dirichlet_distribution
gptkb:symmetric_Dirichlet_distribution
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https://www.w3.org/2000/01/rdf-schema#label
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Dirichlet distribution
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gptkbp:meaning
|
alpha_i / sum(alpha)
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gptkbp:namedAfter
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gptkb:Peter_Gustav_Lejeune_Dirichlet
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gptkbp:normalizationConstant
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multivariate Beta function
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gptkbp:parameter
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alpha vector
concentration parameter
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gptkbp:probabilityDensityFunction
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f(x;α) = (1/B(α)) ∏ x_i^{α_i-1}
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gptkbp:relatedTo
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gptkb:Gamma_distribution
gptkb:Dirichlet_process
gptkb:Latent_Dirichlet_Allocation
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gptkbp:supports
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K-dimensional probability simplex
x_i ≥ 0, sum(x_i) = 1
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gptkbp:type
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continuous distribution
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gptkbp:usedIn
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gptkb:machine_learning
Bayesian statistics
topic modeling
|
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gptkbp:variant
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(alpha_i*(sum(alpha)-alpha_i)) / (sum(alpha)^2*(sum(alpha)+1))
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gptkbp:bfsParent
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gptkb:Peter_Gustav_Lejeune_Dirichlet
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gptkbp:bfsLayer
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5
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