9 papers
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…
Bayesian inference with sources of uncertainty: from confidence modelling to sparse estimation
Rafael Mouallem Rosa, Julyan Arbel, Hien Duy Nguyen
We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mec…
Shifted asymmetric Laplace mixtures of experts
Sphiwe B. Skhosana, Hien Duy Nguyen
Mixtures of experts (MoE) models provide a flexible framework for modelling heterogeneity in data for regression and model-based clustering and classification. MoE models for regre…
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…