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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY: Learning Low-Dimensional Metrics - Robert Nowak (
University of Wisconsin-Madison\; Toyota Technolog
ical Institute )
DTSTART;TZID=Europe/London:20180320T090000
DTEND;TZID=Europe/London:20180320T100000
UID:TALK102568AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102568
DESCRIPTION:This talk discusses the problem of learning a low-
dimensional Euclidean metric from distance compari
sons. Specifically\, consider a set of n items wit
h high-dimensional features and suppose we are giv
en a set of (possibly noisy) distance comparisons
of the form sign(dist(x\,y) &minus\; dist(x\,z))\,
where x\, y\, and z are the features associated w
ith three such items. The goal is to learn the dis
tance function that generates such comparisons. Th
e talk focuses on several key issues pertaining to
the theoretical foundations of metric learning: 1
) optimization methods for learning general low-di
mensional (low-rank) metrics as well as sparse met
rics\; 2) upper and lower (minimax) bounds on pred
iction error\; 3) quantification of the sample com
plexity of metric learning in terms of the dimensi
on of the feature space and the dimension/rank of
the underlying metric\; 4) bounds on the accuracy
of the learned metric relative to the underlying t
rue generative metric. Our results involve novel m
athematical approaches to the metric learning prob
lem and shed new light on the special case of ordi
nal embedding (aka non-metric multidimensional sca
ling). This is joint work with Lalit Jain and Bl
ake Mason.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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