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Theory of Computing Seminar

Friday, April 22, 2016
12:00pm to 1:00pm
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Annenberg 213
Information-theoretic bounds and phase transitions in community detection and high-dimensional clustering
Cristopher Moore, Santa Fe Institute,

Over the past decade, a rich interaction has grown up between
statistical physics and statistical inference.  In particular, physics
often predicts phase transitions where, if a data set becomes too sparse
or too noisy, it suddenly becomes impossible to find its underlying
structure, or even to distinguish it from a "null model" with no
structure at all.  For instance, in the community detection problem in
networks, there is a transition below which the vertices cannot be
labeled better than chance, and the network cannot be distinguished from
an Erdos-Renyi random graph.  Similarly, in the clustering problem in
Gaussian mixture models, it becomes impossible to find the clusters, or
even to tell whether clusters exist, i.e., to distinguish the data from
a single Gaussian.

Many of the physics predictions have been made rigorous, but there is
still a very lively interchange between the fields, both about these
transitions and about asymptotically optimal algorithms.  In particular,
while efficient message-passing and spectral algorithms are known that
succeed down to the so-called Kesten-Stigum bound, in a number of
problems we believe that it is information-theoretically possible (but
perhaps not computationally feasible) to go further.  I will give a
friendly introduction to this field, and present some new results
proving this conjecture.

This is joint work with Jess Banks, Joe Neeman, Praneeth Netrapalli, and
Jiaming Xu. 

For more information, please contact Thomas Vidick by email at [email protected].