71 citations · 110 across the 48 of their papers we have counts for
56 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…
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…
PanIC: consistent information criteria for general model selection problems
Hien Duy Nguyen
Model selection is a ubiquitous problem that arises in the application of many statistical and machine learning methods. In the likelihood and related settings, it is typical to us…
Finite sample inference for empirical Bayesian methods
Hien D Nguyen, Mayetri Gupta
In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real-life problems, especially in c…
Universal inference with composite likelihoods
Hien D Nguyen, Jessica Bagnall-Guerreiro, Andrew T Jones
Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable j…
Non-asymptotic model selection in block-diagonal mixture of polynomial experts models
TrungTin Nguyen, Faicel Chamroukhi, Hien Duy Nguyen +1
Model selection, via penalized likelihood type criteria, is a standard task in many statistical inference and machine learning problems. Progress has led to deriving criteria with…
A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models
TrungTin Nguyen, Hien Duy Nguyen, Faicel Chamroukhi +1
Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this w…
Order selection with confidence for finite mixture models
Hien D Nguyen, Daniel Fryer, Geoffrey McLachlan
The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing…
Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models
Hien Duy Nguyen, TrungTin Nguyen, Faicel Chamroukhi +1
Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving densen…
Universal Inference with Composite Likelihoods
Hien Duy Nguyen
Wasserman et al. (2020, PNAS, vol. 117, pp. 16880-16890) constructed estimator agnostic and finite-sample valid confidence sets and hypothesis tests, using split-data likelihood ra…
Finite sample inference for generic autoregressive models
Hien Duy Nguyen
Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hy…
Non-asymptotic oracle inequalities for the Lasso in high-dimensional mixture of experts
TrungTin Nguyen, Hien D Nguyen, Faicel Chamroukhi +1
We investigate the estimation properties of the mixture of experts (MoE) model in a high-dimensional setting, where the number of predictors is much larger than the sample size, an…
Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces
TrungTin Nguyen, Faicel Chamroukhi, Hien D Nguyen +1
The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We prove the following results: to…
A binary-response regression model based on support vector machines
Hien D Nguyen, Daniel V Fryer
The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization pr…
Regularized Estimation and Feature Selection in Mixtures of Gaussian-Gated Experts Models
Faïcel Chamroukhi, Florian Lecocq, Hien D. Nguyen
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They a…
Approximate Bayesian computation via the energy statistic
Hien D. Nguyen, Julyan Arbel, Hongliang Lü +1
Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely u…
Concentration-based confidence intervals for U-statistics
Hien D. Nguyen
Concentration inequalities have become increasingly popular in machine learning, probability, and statistical research. Using concentration inequalities, one can construct confiden…