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Regularized modified log-Sobolev inequalities, and comparison of Markov chains

Konstantin Tikhomirov, Georgia Institute of Technology

Abstract: In this work, we develop a comparison procedure for the Modified log-Sobolev Inequality (MLSI) constants of two reversible Markov chains on a finite state space. As an application, we provide a sharp estimate of the MLSI constant of the switch chain on the set of simple bipartite regular graphs of size n with a fixed degree d. Our estimate implies that the total variation mixing time of the switch chain is of order O(n log(n)). The result is optimal up to a multiple…

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Geometric EDA for Random Objects

Paromita Dubey, University of Southern California

Abstract: In this talk I will propose new tools for the exploratory data analysis of data objects taking values in a general separable metric space. First, I will introduce depth profiles, where the depth profile of a point ωin the metric space refers to the distribution of the distances between ω and the data objects. I will describe how depth profiles can be harnessed to define transport ranks, which capture the centrality of each element in the metric space with…

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