11 papers
On the minimax-rate optimality of approximate Bayesian computation in nonparametric problems
Hien Duy Nguyen
Approximate Bayesian computation (ABC) replaces likelihood evaluation by simulation and comparison of observed and synthetic data. We establish minimax-rate guarantees for nonparam…
Consistency of variational approximations under bounded Kullback--Leibler divergence
Hien Duy Nguyen, Jacob Westerhout, Thomas Guilmeau +1
Variational methods are widely used to approximate posterior distributions in Bayesian inference when exact computation is infeasible. We study when such approximations inherit pos…
On rates of convergence for sample average approximations without smoothness
Hien Duy Nguyen, Jacob Westerhout, Xin Guo
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate the…
Revisiting Incremental Stochastic Majorization-Minimization Algorithms with Applications to Mixture of Experts
TrungKhang Tran, TrungTin Nguyen, Gersende Fort +5
Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repe…
Statistical process control via -values
Hien Duy Nguyen, Dan Wang
We study statistical process control (SPC) through charting of -values. When in control (IC), any valid sequence is super-uniform, a requirement that can hold in n…
Approximation rates for finite mixtures of location-scale models and fast least-squares estimators
Hien Duy Nguyen, TrungTin Nguyen, Jacob Westerhout +1
Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies…
Modifications of the BIC for order selection in finite mixture models
Hien Duy Nguyen, TrungTin Nguyen
Finite mixture models are ubiquitous in modern statistical modeling, and a recurring practical issue is choosing the model order. In \citet[Sankhyā Series A, \textbf62, pp. 49--66]…
Continuity conditions weaker than lower semi-continuity
Jacob Westerhout, Xin Guo, Hien Duy Nguyen
Lower semi-continuity (\texttt{LSC}) is a critical assumption in many foundational optimisation theory results; however, in many cases, \texttt{LSC} is stronger than necessary. Thi…
Variable selection via thresholding
Ka Long Keith Ho, Hien Duy Nguyen
Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero,…
On the large-sample limits of some Bayesian model evaluation statistics
Hien Duy Nguyen, Mayetri Gupta, Jacob Westerhout +1
Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves informati…
Risk Bounds for Mixture Density Estimation on Compact Domains via the -Lifted Kullback--Leibler Divergence
Mark Chiu Chong, Hien Duy Nguyen, TrungTin Nguyen
We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce t…