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CATEGORIES:Colloquia / Seminar / Lecture
DESCRIPTION:In this talk\, I will review recent work on the use of low-rank
tensor models in multivariate probability\, density estimation\, supervise
d learning\, and combinatorial optimization. We have recently shown that it
is possible to learn high-order but low-rank multivariate distributions fr
om low-order marginals\, and that every multivariate categorical distributi
on can be generated by a (so-called) "naive" Bayes model. As it turns out\,
many real-life datasets can be fitted using distributions of very low rank
. We have also proposed viewing sampling and supervised learning / system i
dentification problems through the lens of low-rank tensor completion\, whi
ch affords parsimonious modeling and sample-efficient learning with identif
ication guarantees. Our most recent work explores the interplay between te
nsors and combinatorial optimization: it shows that every NP-complete probl
em can be cast as an instance of computing the minimum element of a tensor
from its (two) rank-one factors. This exemplifies the modeling power of ver
y low-rank tensors\, and it also opens the door to a continuous multilinear
problem relaxation whose empirical performance on the classic partition pr
oblem and other combinatorial optimization problems appears to be promising
.
DTEND:20230203T170000Z
DTSTAMP:20241106T220155Z
DTSTART:20230203T160000Z
LOCATION:SEC 1.413
SEQUENCE:0
SUMMARY:Tensors in statistical learning and combinatorial optimization
UID:tag:localist.com\,2008:EventInstance_42242893270679
URL:https://events.seas.harvard.edu/event/tensors_in_statistical_learning_a
nd_combinatorial_optimization
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