6 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…
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…
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…
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…
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…