CIS & MINDS Seminar - Rishi Sonthalia

<p>Recorded Seminar:</p><p><br></p><p><a href="https://wse.zoom.us/rec/share/50fBCry0B9draOsObJgAwuO2OQJvMhVaIuAXERghHL... Zoom Meeting:</p><br><a href="https://wse.zoom.us/j/93822965644?pwd=dDNHYVZGY096QU9Dem45STBsQWQ2dz09">... Sonthalia, PhD</b><b> </b></p><p>Assistant Adjunct Professor </p><p>UCLA</p><p><b>“Metric Constrained Problems:Optimization and Applications to Embedding Data”</b></p><br><p><b>Abstract:</b>  Many important machine learningproblems can be formulated as highly constrained convex optimization problems. One importantexample is metric constrained problems. In this talk, we show that standardoptimization techniques can not be used to solve metric constrained problem. Tosolve such problems, we provide a general active set framework, called Projectand Forget, and several variants thereof that use Bregman projections. Projectand Forget is a general purpose method that can be used to solve highly constrainedconvex problems with many (possibly exponentially) constraints. We provide atheoretical analysis of Project and Forget and prove that our algorithmsconverge to the global optimal solution and have a linear rate of convergence.We demonstrate that using our method, we can solve large problem instances ofgeneral weighted correlation clustering, metric nearness, information theoreticmetric learning and quadratically regularized optimal transport; in each case,out-performing the state of the art methods with respect to CPU times andproblem sizes.</p><p> </p><p>We also look at two examples of metric constrained problemsto understand the robustness of Multidimensional Scaling and a methodfor learning hyperbolic embeddings. </p><p> </p><p> </p><p><b>Biography:</b> Rishi Sonthalia, PhD is a Hedrick Assistant Adjunct Professor atUCLA under Andrea Bertozzi, Jacob Foster, and Guido Montufar . Sr. Sonthaliaobtained his Ph.D. in Applied and Interdisciplinary Mathematics from theUniversity of Michigan. His advisors were Anna C. Gilbert and Raj RaoNadakuditi. He did his undergrad at Carnegie Mellon University where heobtained a B.S. in Discrete Math and Computer Science.</p><p> </p><p>Dr. Sonthaliais interested in using Math to develop and analyze tools and algorithms fordata science and machine learning.</p>