Cramér Rate Function in Statistical Estimation: Properties, Models and Algorithms
Yakov Vaisbourd Yakov Vaisbourd Postdoctoral researcher in the Mathematics and Statistics department, McGill University, Canada.
in the Mathematics and Statistics department, McGill University, Canada.
Thursday, Feb 22, 2022, 14:00 PM via zoom
Abstract:
The maximum entropy on the mean (MEM) is an information driven criterion that quantifies the compliance of a given point with a reference probability measure. Thus, it can be naturally utilized for statistical estimation purposes. Even though the MEM function admits a definition in a variational form, it coincides with the Cramér rate function, under reasonable conditions. The latter, mostly known for its role in large deviation theory, admits a closed form expression or can be efficiently evaluated in many practical scenarios. In this work, we further generalize and complement the equivalence between the two functions, encompassing most of the widely used probability distributions. Based on this relation, we propose a class of Bregman proximal gradient methods for solving the optimization formulations that arise in the MEM statistical estimation framework. These types of methods leverage the structure in the problem instance, thus resulting in a significant efficiency improvement compared to general purpose solvers. We illustrate the applicability of the MEM framework for a wide family of linear models and provide an optimization toolbox for this class of problems.
This talk is based on a joint work with Rustum Choksi, Ariel Goodwin, Tim Hoheisel and Carola-Bibiane Schönlieb.
Bio:
Yakov Vaisbourd received his PhD from the Faculty of Industrial Engineering and Management in the Technion under the supervision of Prof. Amir Beck. Since then, he held postdoctoral positions in the school of mathematical sciences, Tel Aviv University, Faculty of Electrical Engineering, Technion and is currently a postdoctoral researcher in the Mathematics and Statistics department, McGill University, Canada.
His research interests fall within the field of continuous optimization with an emphasis on theory, algorithms, and applications. In particular, his work focuses on first order and decomposition methods which are particularly suitable for solving contemporary large-scale problems.
