Wednesday, April 23, 2014 at 3:00pm
Frank H. T. Rhodes Hall, 253
Fulkerson Lectures: Dimitris Bertsimas (MIT) - Classical multivariate statistics via a modern optimization lens
Key problems of classification and regression can naturally be written as optimization problems. While continuous optimization approaches has had a significant impact in statistics, discrete optimization has played a very limited role, primarily based on the belief that mixed integer optimization models are computationally intractable. While such beliefs were accurate two decades ago, the field of discrete optimization has made very substantial progress.
We apply modern first order optimization methods to find feasible solutions for classical problems in statistics, and mixed integer optimization to improve the solutions and to prove optimality by finding matching lower bounds.
Specifically, we report results for the classical variable selection problem in regression currently solved by LASSO heuristically, least quantile regression, factor analysis and optimal CART. In all cases we demonstrate that the solutions found by modern optimization methods outperform the classical approaches. Most importantly, this body of work suggests that the belief widely held in statistics that mixed integer optimization is not practically relevant for statistics applications needs to be revisited.
Joint work with Rahul Mazumder and Angie King.