57 citations · 432 across the 81 of their papers we have counts for
13 papers · 1 filter
Minimax Optimal Rate for Parameter Estimation in Multivariate Deviated Models
Dat Do, Huy Nguyen, Khai Nguyen +1
We study the maximum likelihood estimation (MLE) in the multivariate deviated model where the data are generated from the density function $(1-λ^{\ast})h_{0}(x)+λ^{\ast}f(x|μ^{\ast…
Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models
Tudor Manole, Nhat Ho
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard l…
Entropic Gromov-Wasserstein between Gaussian Distributions
Khang Le, Dung Le, Huy Nguyen +3
We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, whi…
Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel
Nhat Ho, Stephen G. Walker
Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regress…
Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models
Tudor Manole, Nhat Ho
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models w…
A Diffusion Process Perspective on Posterior Contraction Rates for Parameters
Wenlong Mou, Nhat Ho, Martin J. Wainwright +2
We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and t…
Convergence Rates for Gaussian Mixtures of Experts
Nhat Ho, Chiao-Yu Yang, Michael I. Jordan
We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood…
Sharp Analysis of Expectation-Maximization for Weakly Identifiable Models
Raaz Dwivedi, Nhat Ho, Koulik Khamaru +3
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on i.i.d. samples are known to have lower accuracy than t…
On posterior contraction of parameters and interpretability in Bayesian mixture modeling
Aritra Guha, Nhat Ho, XuanLong Nguyen
We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model it…
Singularity, Misspecification, and the Convergence Rate of EM
Raaz Dwivedi, Nhat Ho, Koulik Khamaru +3
A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly…
Robust estimation of mixing measures in finite mixture models
Nhat Ho, XuanLong Nguyen, Ya'acov Ritov
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popu…
Singularity structures and impacts on parameter estimation in finite mixtures of distributions
Nhat Ho, XuanLong Nguyen
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for whi…
Identifiability and optimal rates of convergence for parameters of multiple types in finite mixtures
Nhat Ho, XuanLong Nguyen
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. Fir…