Event

Long Nguyen (University of Michigan)

Friday, October 19, 2018 15:30to16:30
Burnside Hall Room 1104, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Multilevel clustering and optimal transport

Abstract:

Optimal transport plays an increasingly relevant and useful role in the theory and application of mixture model based clustering and inference. In this talk I will describe some recent progress in characterizing the convergence behavior of mixing distributions when one fits a mixture model to the data. This theory hinges on the relationship between the space of mixture densities, which is endowed with variational or Hellinger distance, and the space of mixing measures endowed with optimal transport distance metrics. Next, I will introduce an optimal transport based technique for the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures. 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. Some theoretical and experimental results will be presented.

Speaker

Long Nguyen is an Associate Professor in the Department of Statistics at the University of Michigan. His research interests include nonparametric Bayesian statistics; hierarchical, mixture and graphical models; spatiotemporal and functional data analysis; stochastic, variational and geometric methods in statistical inference.

Organized by theMcGill Statistics Group

Seminar website:https://mcgillstat.github.io/

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