BEGIN:VCALENDAR VERSION:2.0 PRODID:-//University of California\, Berkeley//UCB Events Calendar//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 DTSTART:19701029T020000 RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU END:STANDARD BEGIN:DAYLIGHT DTSTART:19700402T020000 TZOFFSETFROM:-0800 TZOFFSETTO:-0700 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT DTSTAMP:20190225T081010Z DTSTART;TZID=America/Los_Angeles:20190226T150000 DTEND;TZID=America/Los_Angeles:20190226T170000 TRANSP:OPAQUE SUMMARY:Sparse Generalized Eigenvalue Problem and its Application in Neuroscience ORGANIZER;CN="UC Berkeley Calendar Network": LOCATION:5101 Berkeley Way West DESCRIPTION:Kean Ming Tan\, PhD\, School of Statistics\, University of Minnesota\n\nSparse generalized eigenvalue problem (GEP) plays a pivotal role in a large family of high-dimensional learning tasks\, including sparse Fisher’s discriminant analysis\, canonical correlation analysis\, and sufficient dimension reduction. Most of the existing methods and theory in the context of specific statistical models that can be recast into sparse GEP require restrictive structural assumptions on the input matrices. This talk will focus on a two-stage computational framework for solving the sparse GEP. At the first stage\, we solve a convex relaxation of the sparse GEP. Taking the solution as an initial value\, we then exploit a non-convex optimization perspective and propose the truncated Rayleigh flow method (Rifle) to estimate the leading generalized eigenvector\, and show that it converges linearly to a solution with the optimal statistical rate of convergence. Theoretically\, our method significantly improves upon the existing literature by eliminating the structural assumptions on the input matrices. Numerical studies in the context of several statistical models are provided to validate the theoretical results. We then apply the proposed method on an electrocorticography dataset to understand how human brains recall sequences of words. URL: SEQUENCE:0 CLASS:PUBLIC CREATED:20190225T081010Z LAST-MODIFIED:20190225T081010Z X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-OWNERAPPTID:-1 END:VEVENT END:VCALENDAR