## ARC Colloquium: Anup Rao - Yale University

(Refreshments will be served in Klaus 2222 at 2 pm)

Title:
Algorithms for Lipschitz Learning on Graphs

Abstract:
We develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. The extension we compute is the absolutely minimal Lipschitz extension, and is the limit for large p of p-Laplacian regularization. We present an algorithm that computes a minimal Lipschitz extension in expected linear time, and an algorithm that computes an absolutely minimal Lipschitz extension in expected time O(mn). The latter algorithm has variants that seem to run much faster in practice. These extensions are particularly amenable to regularization: we can perform l_0 regularization on the given values in polynomial time and l_1 regularization on the graph edge weights in time O(m^(3/2)). Our algorithms naturally extend to directed graphs.  This is a joint work with Rasmus Kyng, Sushant Sachdeva and Daniel Spielman.

#### Event Details

Date/Time:

• Monday, March 30, 2015
1:00 pm - 2:00 pm
Location: Klaus Room 1116 West

#### For More Information Contact

Dani Denton

denton at cc dot gatech dot edu