**Abstract: **Given a set of distances amongst points, determining what metric representation is most “consistent” with the input distances or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. In this talk, we discuss a number of variants of this problem, from convex optimization problems with metric constraints to sparse metric repair.

**Bio: **Anna C. Gilbert is Professor of Mathematics and Statistics and Data Science. Gilbert received her Bachelor of Science degree from the University of Chicago and a Ph.D. from Princeton University, both in Mathematics. In 1997, she was a postdoctoral fellow at Yale University and AT&T Labs-Research. From 1998 to 2004, she was a member of technical staff at AT&T Labs-Research in Florham Park, NJ. From 2004 to 2020, she was with the Department of Mathematics (with a secondary appointment in Electrical and Computer Engineering) at the University of Michigan, where she was appointed the Herman H. Goldstine Collegiate Professor. In 2020, she joined Yale University as the John C. Malone Professor of Mathematics and Professor of Statistics & Data Science. She has received several awards, including a Sloan Research Fellowship (2006), an NSF CAREER award (2006), the National Academy of Sciences Award for Initiatives in Research (2008), the Association of Computing Machinery (ACM) Douglas Engelbart Best Paper award (2008), the EURASIP Signal Processing Best Paper award (2010), and the SIAM Ralph E. Kleinman Prize (2013). Her research interests include analysis, probability, discrete mathematics, and algorithms. She is especially interested in randomized algorithms with applications to harmonic analysis, signal and image processing, and massive datasets.