Hi!!! I am currently a postdoctoral fellow in the Electrical Engineering and Computer Science (EECS) Department where I am very fortunate to be mentored by Professor Michael Jordan and Professor Martin Wainwright. Before going to Berkeley, I finished my Phd degree in the Department of Statistics, University of Michigan, Ann Arbor where I am very fortunate to be advised by Professor Long Nguyen and Professor Ya'acov Ritov.

At this moment, I am interested in exploring potential applications of optimal transport theory to understand challenging problems in machine learning and deep learning. Two major directions that I am currently working are statistical and computational efficiency of mixture and hierarchical models as well as scalable models to study complex and large data.

For a recent version of my CV, please email me via minhnhat@berkeley.edu.

Educational background:

- 2017 - present : Postdoctoral Fellow in EECS Department, University of California, Berkeley
- 2012 - 2017 : PhD in Statistics, University of Michigan, Ann Arbor
- 2007 - 2011 : BS in Mathematics and Computer Science (highest distinction), Ho Chi Minh University of Science, Vietnam.

Current research interests:

- Bayesian nonparametrics
- Mixture and hierarchical models, graphical models
- Statistical learning theory
- Multiple testing hypotheses
- Causal inference
- Deep learning
- Robust statistics

Theses and Reports:

- Nhat Ho. Parameter estimation and multilevel clustering
with mixture and hierarchical models .
*Phd Thesis, University of Michigan, Ann Arbor, 2017 (343 pages).* - Nhat Ho and XuanLong Nguyen. Identifiability and optimal rates of convergence for parameters of multiple types in finite mixtures .
*95 pages, Technical report 536, Department of Statistics, University of Michigan, Ann Arbor, January 2015*

Journal Publications:

- Nhat Ho and XuanLong Nguyen. On strong identifiability and convergence rates of
parameter estimation in finite mixtures .
*Electronic Journal of Statistics*, 10(1), 271-307, 2016.__Summary__: This paper studies identifiability and convergence behaviors for parameters of multiple types, including matrix-variate ones, that arise in finite mixtures, and the effects of model fitting with extra mixing components. We consider several notions of strong identifiability in a matrix-variate setting, and use them to establish sharp inequalities relating the distance of mixture densities to the Wasserstein distances of the corresponding mixing measures. Characterization of identifiability is given for a broad range of mixture models commonly employed in practice, including locationcovariance mixtures and location-covariance-shape mixtures, for mixtures of symmetric densities, as well as some asymmetric ones. Minimax lower bounds and rates of convergence for the maximum likelihood estimates are established for such classes, which are also confirmed by simulation studies. - Nhat Ho and XuanLong Nguyen. Convergence rates of parameter estimation for some weakly identifiable finite mixtures .
*Annals of Statistics, 2016*, 44(6), 2726-2755, 2016.__Summary__: We establish minimax lower bounds and maximum likelihood convergence rates of parameter estimation for mean-covariance multivariate Gaussian mixtures, shape-rate Gamma mixtures, and some variants of finite mixture models, including the setting where the number of mixing components is bounded but unknown. These models belong to what we call ”weakly identifiable” classes, which exhibit specific interactions among mixing parameters driven by the algebraic structures of the class of kernel densities and their partial derivatives. Accordingly both the minimax bounds and the maximum likelihood parameter estimation rates in these models are shown to be typically much slower than the usual $n^{-1/2}$ or $n^{-1/4}$ rates of convergence. - Nhat Ho and XuanLong Nguyen. Singularity structures and impacts on parameter estimation behavior in finite mixtures of distributions .
*Under review.*- Technical report version that contains all the missing results in the journal version: Singularity structures and impacts on parameter estimation behavior in finite mixtures of distributions .
*85 pages.*

__Summary__: Singularities of a statistical model are the elements of the model’s parameter space which make the corresponding Fisher information matrices degenerate. These are the points for which standard estimation techniques such as the maximum likelihood estimator do not admit the root-n parametric rate of convergence. We propose a general framework for the identification of singularity structures of the parameter space of finite mixtures, and study the impact of the singularity levels on minimax lower bounds and rates of convergence for the maximum likelihood estimator over a compact parameter space. Our investigation makes explicit the deep links between model singularities, parameter estimation rates and minimax bounds, and the algebraic geometry of the parameter space for mixtures of continuous distributions. The theory is applied to establish concrete convergence rates of parameter estimation for finite mixture of skewnormal distributions. This rich and increasingly popular model class is shown to exhibit a remarkably complex range of asymptotic behaviors that have not been hitherto reported in literature. - Technical report version that contains all the missing results in the journal version: Singularity structures and impacts on parameter estimation behavior in finite mixtures of distributions .
- Nhat Ho, XuanLong Nguyen, Mikhail Yurochkin, Hung Hai Bui, Viet Huynh, and Dinh Phung. Multilevel clustering via Wasserstein means .
*Proceedings of the ICML, 2017.*- Code for all the experiments in the paper is available at: Multilevel_Wasserstein_means .

__Summary__: We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a large hierarchically structural corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with the Wasserstein distance metric. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. We also establish consistency properties enjoyed by our estimates of both local and global clusters. Finally, we present experiment results with both synthetic and real data to demonstrate the flexibility and scalability of the proposed approach. - Nhat Ho, XuanLong Nguyen, Ya'acov Ritov. Robust estimation of mixing measures in finite mixture models .
*Under review.*__Summary__: 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 popular approach is to choose some kernel functions that we empirically believe our data are generated from and use these kernels to fit our models. Nevertheless, as long as the chosen kernel and the true kernel are different, statistical inference of mixing measure under this setting will be highly unstable. To overcome this challenge, we propose flexible and efficient robust estimators of the mixing measure in these models, which are inspired by the idea of minimum Hellinger distance estimator, model selection criteria, and superefficiency phenomenon. We demonstrate that our estimators consistently recover the true number of components and achieve the optimal convergence rates of parameter estimation under both the well- and mis-specified kernel settings for any fixed bandwidth. These desirable asymptotic properties are illustrated via careful simulation studies with both synthetic and real data.

Conferences, Seminars, and Workshops Presentations:

- Singularity Structure of Parameter Space and Posterior Contraction in Finite Mixture Models.
*Joint Statistical Meetings (JSM), August, 2017, Baltimore, Maryland.* - Singularity structures and parameter estimation behavior in finite mixtures of distributions.
*Nonparametric Statistics Workshop: Integration of Theory, Methods, and Applications, October, 2016, Ann Arbor, Michigan.* - Singularity structures and impacts on parameter estimation in finite mixtures of distributions.
*Shannon Centennial Symposium, September, 2016, Ann Arbor, Michigan.* - Singularity structures and parameter estimation behavior in finite mixtures of distributions.
*Joint Statistical Meetings (JSM), August, 2016, Chicago, Illinois.* - Singularity structures and parameter estimation behavior in finite mixtures of distributions.
*Conference on Statistical Learning and Data Science, June, 2016, University of North Carolina at the Chapel Hill.* - Singularity structures and parameter estimation behavior in finite mixtures of distributions.
*Statistical Machine Learning Student Workshop, June, 2016, University of Michigan, Ann Arbor.* - Singularity structures and parameter estimation in mixtures of skew normal distributions.
*Michigan Student Symposium for Interdisciplinary Statistical Sciences (MSSISS), March, 2016, Ann Arbor, MI.* - Weak identifiability and convergence rate of mixing measures in over-fitted Gaussian mixture models.
*Student Seminar, Department of Statistics, University of Michigan, January, 2016, Ann Arbor, Michigan.* - Intrinsic difficulties for the inference of mixing measures in finite mixtures of
univariate skew normal distributions.
*From Industrial Statistics to Data Science, October, 2015, Ann Arbor, Michigan.* - Posterior concentration of mixing parameters in some weakly identifiable finite
mixture models.
*10th Conference on Bayesian Nonparametrics, June, 2015, Raleigh, North Carolina* - Weak identifiability and optimal rate of convergence of mixing measures in over-fitted Gaussian mixture models.
*Statistical Machine Learning Student Workshop, June, 2015, University of Michigan, Ann Arbor* - Weak identifiability and optimal rate of convergence of mixing measures in
over-fitted Gaussian mixture models.
*NSF Conference - Statistics for Complex Systems, June, 2015, Madison, Wisconsin* - Optimal convergence rate of parameter estimation in overfitted finite Gaussian
mixture models.
*Michigan Student Symposium for Interdisciplinary Statistical Sciences (MSSISS), March, 2015, Ann Arbor, MI* - Identifiability and convergence rate of parameter estimations in exact-fitted finite
mixture models.
*Statistical Machine Learning Student Workshop, June, 2014, University of Michigan, Ann Arbor*

Selected Honors and Awards:

- Conference on Statistical Learning and Data Science Travel Award, UNC Chapel Hill, 2016.
- Best Poster Award Michigan Student Symposium for Interdisciplinary Statistical Sciences, 2016.
- NSF Conference for Complex Systems Poster Award, 2015.
- Rackham School of Graduate Studies Conference Travel Award, 2015, 2016, 2017.
- Departmental Fellowship, University of Michigan, Ann Arbor, 2012-2013.
- Highest Distinction Graduation, Ho Chi Minh University of Science, 2011.
- Odon Vallet Scholarship, Ho Chi Minh University of Science, 2008-2011.
- Outstanding Student Scholarship, Department of Mathematics and Computer Science, Ho Chi Minh University of Science, 2008-2011.

Reviewers:

- Annals of Statistics.
- Bernoulli.
- Electronic Journal of Statistics.
- International Conference on Machine Learning (ICML).
- Neural Information Processing Systems (NIPS).

Professional Services:

- Student Assistant of the Nonparametric Statistics Workshop: Integration of Theory, Methods, and Applications, October 2016, Ann Arbor, Michigan
- Student Assistant of the Extreme Value Analysis Conference (EVA), Ann Arbor, Michigan, June 2015.

Current collaborators: Long Nguyen, Ya'acov Ritov, Michael Jordan, Martin Wainwright, Richard Baraniuk, Anima Anandkumar , Natesh Pillai , Avi Feller , Peng Ding , Ankit Patel, Will Fithian, Hung Bui, Dinh Phung , Mikhail Yurochkin , Viet Huynh , Aritra Guha , Chiao-Yu Yang , Tan Nguyen, Lihua Lei , Raaz Dwivedi , Koulik Khamaru, Joseph Borja, Yuting Wei.

Number of page view: