BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anna C. Gilbert (Yale University) DTSTART:20210113T180000Z DTEND:20210113T190000Z DTSTAMP:20260423T003237Z UID:MPML/27 DESCRIPTION:Title: Me tric representations: Algorithms and Geometry\nby Anna C. Gilbert (Yal e University) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract\nGiven a set of distances amongst points\, determin ing what metric representation is most "consistent" with the input distanc es 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 focus on 3 specific metric constrained problems\, a class of optimization problems with metric constraints: metric nearness (Brickell et al. (2008) )\, weighted correlation clustering on general graphs (Bansal et al. (2004 ))\, and metric learning (Bellet et al. (2013)\; Davis et al. (2007)).\n\n Because of the large number of constraints in these problems\, however\, t hese and other researchers have been forced to restrict either the kinds o f metrics learned or the size of the problem that can be solved. We provid e an algorithm\, PROJECT AND FORGET\, that uses Bregman projections with c utting planes\, to solve metric constrained problems with many (possibly e xponentially) inequality constraints. We also prove that our algorithm con verges to the global optimal solution. Additionally\, we show that the opt imality error decays asymptotically at an exponential rate. We show that u sing our method we can solve large problem instances of three types of met ric constrained problems\, out-performing all state of the art methods wit h respect to CPU times and problem sizes.\n\nFinally\, we discuss the adap tation of PROJECT AND FORGET to specific types of metric constraints\, nam ely tree and hyperbolic metrics.\n LOCATION:https://researchseminars.org/talk/MPML/27/ END:VEVENT END:VCALENDAR