Extra Colloquium Mathematics - Max Welling

Join us for coffee and tea at 15.45 p.m.

 

Date: Thursday, March 17^th 2011

Speaker: Max Welling

Room: 5161.0289 (Bernoulliborg),

Time: 16.15

 

 

Title: Herding: Learning with Weakly Chaotic Nonlinear Dynamical Systems

Abstract:

 

We describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These ``herding systems'' combine learning and inference into one algorithm. They convert moments directly into a sequence of pseudo-samples without learning an explicit model. Using the "perceptron cycling theorem" we can easily show that Monte Carlo estimates based on these pseudo-samples converge at an optimal rate of O(1/T), due to infinite range negative auto-correlations. We show that the information content of these sequences, as measured by sub-extensive entropy, can grow as fast as  K log(N), which is faster than the usual 1/2 K log(N) for sequences generated by random posterior sampling from a Bayesian posterior model. In continuous spaces we can control an infinite number of moments
by formulating herding in a Hilbert space. Also in this case sample averages over arbitrary functions in the Hilbert space will converge at an optimal rate of O(1/T).
More generally, we advocate the application of the rich theoretical framework of nonlinear dynamical systems and chaos theory to statistical learning.

 

 

 

 

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. M. Dür (e-mail: M.E.Dur@rug.nl)