BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Venkat Chandrasekaran (Caltech) DTSTART:20200512T230000Z DTEND:20200513T001500Z DTSTAMP:20260423T024448Z UID:MADDD/3 DESCRIPTION:Title: Fi tting convex sets to data\nby Venkat Chandrasekaran (Caltech) as part of Mathematics of Data and Decisions @ Davis\n\n\nAbstract\nA number of pr oblems in signal processing may be viewed conceptually as fitting a convex set to data. In vision and learning\, the task of identifying a collecti on of features or atoms that provide a concise description of a dataset ha s been widely studied under the title of dictionary learning or sparse cod ing. In convex-geometric terms\, this problem entails learning a polytope with a desired facial structure from data. In computed tomography\, reco nstructing a shape from support measurements arises commonly in MRI\, robo tics\, and target reconstruction from radar data. This problem is usually reformulated as one of estimating a polytope from a collection of noisy h alfspaces.\n\nIn this talk we describe new approaches to these problems th at leverage contemporary ideas from the optimization literature on lift-an d-project descriptions of convex sets. This perspective leads to natural semidefinite programming generalizations of previous techniques for fittin g polyhedral convex sets to data. We provide several stylized illustratio ns in which these generalizations provide improved reconstructions. On th e algorithmic front our methods rely prominently on operator scaling\, whi le on the statistical side our analysis builds on links between learning t heory and semialgebraic geometry.\n LOCATION:https://researchseminars.org/talk/MADDD/3/ END:VEVENT END:VCALENDAR