### DIMACS Theoretical Computer Science Seminar

Title: Learning and testing k-modal distributions

Speaker: ** Rocco Servedio**, Columbia University

Date: Wednesday, April 20, 2011 11:00-12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

A k-modal probability distribution over the domain {1,...,N} is one whose histogram has
at most k "peaks" and "valleys". Such distributions are a natural generalization
of the well-studied class of monotone increasing (or monotone decreasing) probability distributions.

We study the problem of learning an unknown k-modal distribution from samples.
We also study a related problem in property testing: given access to
samples from an unknown k-modal distribution p,
determine whether p is identical to q or p is "far" from q.
Here q is a k-modal distribution which may be given explicitly or may be available via sample access.

We give algorithms for these problems that are provably close to the best
possible in terms of sample and time complexity.
An interesting feature of our approach is that our learning algorithms
use ingredients from property testing and vice versa.

Joint work with Costis Daskalakis and Ilias Diakonikolas.