Abstract: In this talk, we demonstrate that modern convex, robust and especially mixed integer optimization (MIO) methods, when applied to a variety of classical Machine Learning (ML) /Statistics (S) problems can lead to certifiable optimal solutions for large scale instances that have often significantly improved out of sample accuracy compared to heuristic methods used in ML/S.
Specifically
1) We use MIO to solve sparse regression problems solved by Lasso heuristically. Furthermore, we show that robustness and not sparsity is the major reason of the success of Lasso in contrast to widely held beliefs in ML/S.
2) We present Optimal Classification trees solved by CART heuristically.
3) We introduce Stable Regression that uses robust optimization to provide solutions to regression problems that have low output and coefficient variability.

In all cases we demonstrate that optimal solutions to large scale instances (a) can be found in seconds, (b) can be certified to be optimal in minutes and (c) outperform classical approaches. Most importantly, this body of work suggests that linking ML/S to modern optimization will lead to significant advantages.

This seminar is open to all and will be livestreamed via Zoom https://umich.zoom.us/j/94350208889