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[theory-seminar] [theory-lunch] Jacob Steinhardt on Certifying 2->q Norm

Hongyang Zhang hongyang at cs.stanford.edu
Tue Oct 10 15:22:40 PDT 2017


Hi Everyone

This *thursday 12:00pm to 1:00pm, at Gates 463A*, Jacob Steinhardt will
tell us about "Certifying 2-q Norms with Sum-of-Squares". See below for the
abstract.

As usual, the talk starts at 12:30pm. See you all!

-hongyang

------------------------------------------------------------

Title: Certifying 2->q Norm with Sum-of-Squares

Abstract: Approximating the 2->q norm is a natural geometric problem which
is closely related to the unique games conjecture. BBHKSZ12 show that the
sum-of-squares (SOS) hierarchy is able to approximate the 2->q norm well on
points sampled from product distributions on the hypercube, but the general
performance of SOS on 2->q norm is not well-understood. I will show that
for distributions satisfying the *Poincare inequality*, m rounds of
sum-of-squares are sufficient to approximate the 2->m norm for all even m
>= 2. This substantially extends the result of BBHKSZ12. As applications we
present improved algorithms for clustering and robust mean estimation. The
proof exploits recent advances in geometric probability by Adamczak and
Wolff.

This is joint work with Pravesh Kothari.
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