Location: Science park 904, UvA, Amsterdam, lecture room c.1.110

Date: Wednesday, 21st of December 2011

Time: 13.00 - 14.00 hrs.

This talk will start by reviewing some active projects in my research group. In the second half of my talk I will discuss a nonlinear dynamical system's approach to machine learning. In particular I will describe a class of deterministic weakly chaotic dynamical systems with infinite memory. These "herding systems'' combine learning and inference into a single algorithm. They convert moments directly into a sequence of pseudo-samples without learning an explicit model.

Using the "perceptron cycling theorem" one can show that Monte Carlo estimates based on these pseudo-samples converge at an optimal rate of O(1/T). I will argue that the information content of these sequences, as measured by sub-extensive entropy, can grow as fast as K*log(T). 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). The usefulness of this framework will be illustrated with examples in Monte Carlo sampling, classification and image segmentation.