Dirichlet Process Mixture Model Data Object

Dirichlet Process Mixture Model Hyperparameters

GammaNormal(; μ0 = 0.0, λ0 = 1.0, α0 = 1.0, β0 = 1.0)

Normal-Gamma distribution

A Normal-Gamma distribution is the conjugate prior of a Normal distribution with unknown mean and precision.

Paramters

• μ0: location
• λ0 > 0: number of pseudo-observations
• α0 > 0
• β0 > 0

Example:

d = GammaNormal()

Hierarchical Dirichlet Process Mixture Model Hyperparameters

WishartGaussian(μ0, κ0, ν0, Σ0)

Gaussian-inverse-Wishart distribution

A Gaussian-inverse-Wishart distribution is the conjugate prior of a multivariate normal distribution with unknown mean and covariance matrix.

Parameters

• μ0, Dx1: location
• κ0 > 0: number of pseudo-observations
• ν0 > D-1: degrees of freedom
• Σ0 > 0, DxD: scale matrix

Example

julia> (N, D) = size(X)
julia> μ0 = mean(X, dims = 1)
julia> d = WishartGaussian(μ0, 1.0, 2*D, cov(x)) 

add!(d::ConjugatePostDistribution, X)

Add data to Posterior Distribution (inplace).

add(d::ConjugatePostDistribution, X)

Add data to Posterior Distribution.

HDP initialization using random assignments.

Log PMF for BernoulliBeta.

Log PMF for MultinomialDirichlet.

Log PMF for MultinomialDirichlet.

logpostpred(d::ConjugatePostDistribution, X)

Compute log posterior predictive.

point_estimate(psm::Array{Float64, 2})

Find optimal partition which minimizes the lower bound to the Variation of Information obtain from Jensen's inequality where the expectation and log are reversed.

Code based on R implementation by Sara Wade <sara.wade@eng.cam.ac.uk>

posteriorParameters(d::ConjugatePostDistribution)

Compute posterior distribution parameters.

randomindex(p::Vector{Float64})

Randomly select an index propotional to its probability.

remove!(d::ConjugatePostDistribution, X)

Remove data from Posterior Distribution (inplace).

remove(d::ConjugatePostDistribution, X::AbstractArray)

Remove data from Posterior Distribution.

resampleα(α::Float64, N::Int, K::Int)

Resample α given the approach by Escobar and West. (page 585)

abstract Hyperparameters

Abstract Model Buffer Object

Abstract Model Data Object

Hierarchical Dirichlet Process Mixture Model Data Object

Single iteration of collabsed Gibbs sampling using CRP.

Single Gibbs sweep of HDP training using beta variables.

isdistempty(d::ConjugatePostDistribution)

Check if distribution is empty (contains no samples).

point_estimate_avg(psm::Array{Float64, 2})

Find optimal partition which minimizes the lower bound to the Variation of Information obtain from Jensen's inequality where the expectation and log are reversed.

Code based on R implementation by Sara Wade <sara.wade@eng.cam.ac.uk>

Log PDF of Generalized student-t Distribution.

Compute Energy of model for given data

variation_of_information_lb()

Computes the lower bound to the posterior expected Variation of Information.

variation_of_information_lb()

Computes the lower bound to the posterior expected Variation of Information.