6 papers · 1 filter
Closed-form solutions to some generalized variational inference problems
Hien Duy Nguyen, Jacob Westerhout
The Donsker--Varadhan formula characterizes the ordinary Bayesian posterior as the solution of an unrestricted -regularized variational problem. Generalized variationa…
Bounds on the Number of Modes of a Gaussian Mixture Density
Hien Duy Nguyen
We derive explicit upper bounds for the number of nondegenerate critical points of a -component Gaussian mixture density in , and the number of modes when the moda…
Characterisations of Kullback--Leibler approximation by finite Gaussian mixtures
Hien Duy Nguyen
We study the Kullback--Leibler (KL) divergence approximation theory of Gaussian mixture models (GMMs) by isolating an abstract mechanism behind several necessary-and-sufficient sta…
Consistency of the Bayesian Information Criterion for Model Selection in Exploratory Factor Analysis
Hien Duy Nguyen, Kei Hirose
We study model selection by the Bayesian information criterion (BIC) in fixed-dimensional exploratory factor analysis over a fixed finite family of compact covariance classes. Our…
On the identifiability of Dirichlet mixture models
Hien Duy Nguyen, Mayetri Gupta
We study identifiability of finite mixtures of Dirichlet distributions on the interior of the simplex. We first prove a shift identity showing that every Dirichlet density can be w…
Approximation by mixtures of multivariate Erlang distributions
Hien Duy Nguyen
We prove that finite multivariate Erlang mixture densities with a common rate parameter are dense in the class of probability densities on that belong to $L^{p…