Rishi Sonthalia, “Metric Constrained Problems: Optimization and Applications to Embedding Data”
Please join us on Tuesday, March 28, 2023 at 12:00pm in CLARK HALL, Room 110 and on ZOOM for the CIS & MINDS Seminar Series:
Guest: Rishi Sonthalia, PhD
Assistant Adjunct Professor
UCLA
Topic: “Metric Constrained Problems: Optimization and Applications to Embedding Data”
Virtually over Zoom
Join Zoom Meeting:
https://wse.zoom.us/j/93822965644?pwd=dDNHYVZGY096QU9Dem45STBsQWQ2dz09
If you would like to meet with Rishi Sonthalia before or after his seminar, please sign up for a time at this link:
Rishi Sonthalia, PhD
Assistant Adjunct Professor
UCLA
“Metric Constrained Problems: Optimization and Applications to Embedding Data”
Abstract: Many important machine learning problems can be formulated as highly constrained convex optimization problems. One important example is metric constrained problems. In this talk, we show that standard optimization techniques can not be used to solve metric constrained problem. To solve such problems, we provide a general active set framework, called Project and Forget, and several variants thereof that use Bregman projections. Project and Forget is a general purpose method that can be used to solve highly constrained convex problems with many (possibly exponentially) constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithms converge to the global optimal solution and have a linear rate of convergence. We demonstrate that using our method, we can solve large problem instances of general weighted correlation clustering, metric nearness, information theoretic metric learning and quadratically regularized optimal transport; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.
We also look at two examples of metric constrained problems to understand the robustness of Multidimensional Scaling and a method for learning hyperbolic embeddings.
Biography: Rishi Sonthalia, PhD is a Hedrick Assistant Adjunct Professor at UCLA under Andrea Bertozzi, Jacob Foster, and Guido Montufar . Sr. Sonthalia obtained his Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan. His advisors were Anna C. Gilbert and Raj Rao Nadakuditi. He did his undergrad at Carnegie Mellon University where he obtained a B.S. in Discrete Math and Computer Science.
Dr. Sonthalia is interested in using Math to develop and analyze tools and algorithms for data science and machine learning.