BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eitan Levin (UBC-O hosted) (California Institute of Technology) DTSTART:20240125T220000Z DTEND:20240125T230000Z DTSTAMP:20260513T193643Z UID:SFUOR/28 DESCRIPTION:Title: A ny-dimensional Convex Sets\nby Eitan Levin (UBC-O hosted) (California Institute of Technology) as part of PIMS-CORDS SFU Operations Research Sem inar\n\nLecture held in ASB 10908.\n\nAbstract\nClassical algorithms are d efined on inputs of different sizes. In contrast\, data-driven algorithms\ , that is\, algorithms learned from some data\, may only be defined on inp uts of the same size as the data. What\ndoes it mean for an algorithm to b e defined on infinitely-many input sizes? How do we describe such\nalgorit hms\, and how do we parametrize and search over them?\n\nIn this talk\, we tackle these questions for convex optimization-based algorithms. Describi ng such\nalgorithms reduces to describing convex sets. These\, in turn\, a re often "freely" described\, meaning that their description makes instant iation in every dimension obvious. Examples include unit balls of\nstandar d norms defined on vectors of any size\, graph parameters defined for grap hs of any size\, and\n(quantum) information theoretic quantities defined f or distributions on any number of (qu)bits.\n\nWe show that such free desc riptions of convex sets arise from two ingredients. First\, group invarian ce\nand the recently-identified phenomenon of representation stability. Se cond\, embeddings and projections\nrelating different-sized problem instan ces. We combine these ingredients to obtain parametrized\nfamilies of infi nitely instantiable convex sets. To extend a set learned from data in a fi xed dimension to higher ones\, we identify consistency conditions relating sets in different dimensions that are satisfied in a variety of applicati ons\, and obtain parametrizations respecting these conditions. Our paramet rizations can be obtained computationally.\n LOCATION:https://researchseminars.org/talk/SFUOR/28/ END:VEVENT END:VCALENDAR