Inverse bounds for learning latent structures

Thời gian: 14:00 đến 16:00 Ngày 09/06/2022

Địa điểm: Hội trường Laurent Schwartz


Talk title: Inverse bounds for learning latent structures.

Speaker: Nguyen Xuan Long, University of Michigan, Ann Arbor.

Time14:00-16:00, Thursday, June 9, 2022.

Onsite: Speaker will give the talk at VIASM, 157 Chùa Láng, Đống Đa, Hà Nội. 

Online: Participation by the link:

Abstract: Inverse bounds are inequalities that provide upper bound estimates of the distance of latent structures of interest in a suitable Wasserstein space in terms of the statistical distance (e.g., total variation, Hellinger, KL divergence) in the space of data populations. This type of bounds is useful in deriving the rates of parameter estimation (via either M-estimators or Bayesian methods) that arise in latent structured models, including convolution models, mixture models and hierarchical models. These are models that play a major role in modern statistics and data science. In this talk I will present several such optimal transport based inverse bounds for (i) mixing measures in mixture and convolution models, (ii) the de Finetti's mixing measure in mixture of product distributions, and (iii) mixing measures in the settings of contaminated models and regression with heterogeneous responses. The derivation of such inverse bounds requires a deeper investigation into conditions of the latent structure's identifiability, which shed some light about the geometry of latent structured models. 

Bio: Nguyen Xuan Long is Professor of Statistics and of Electrical Engineering and Computer Science at the University of Michigan. His research interests lie in Bayesian nonparametric statistics, machine learning and optimal transport, and analysis of complex structured data. He has served as associate editor in several major journals, including the Annals of Statistics, Bayesian Analysis, SIAM Journal on Mathematics of Data Science and Journal of Machine Learning Research. He is a distinguished associate member of VIASM, and a fellow of the IMS (Institute of Mathematical Statistics).