71 citations · 110 across the 48 of their papers we have counts for
9 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…
Empowering Bayes with sources of uncertainty: from confidence modelling to sparse estimation
Rafael Mouallem Rosa, Julyan Arbel, Hien Duy Nguyen
We introduce sources of uncertainty (SoU) inference, a general framework that extends Bayesian inference by allowing researchers to explicitly encode heterogeneous confidence acros…
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…
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…
A variational framework for modal estimation
Tâm LeMinh, Julyan Arbel, Florence Forbes +1
Multivariate mode estimation arises in many statistical problems such as inverse problems, multimodal sampling, and density-based clustering, but becomes challenging in moderate to…