Mixing

Dana Randall, Georgia Tech.

In this tutorial, we introduce the notion of a Markov chain and explore
how it can be used to sample from a large set of configurations. Our
primary focus is determining how quickly a Markov chain ``mixes,'' or
converges to its stationary distribution, as this is the key factor in
the running time. We provide an overview of several techniques
used to establish good bounds on the mixing time. The
applications are mostly chosen from statistical physics, although the
methods are much more general.

Machine Learning: my favorite
results, directions, and open problems

Avrim Blum, CMU

In this tutorial I will start from scratch and give an introduction to
some of the main themes and results in the theory of machine learning.
I will describe (a biased subset of) some of the main accomplishments
of computational learning theory to date, as well as current
directions and open problems. One of my goals in this tutorial is to
give my sense of why the theory of machine learning is a fundamental
part of the theory of computing, intimately connected to complexity
theory, cryptography, approximation algorithms, and online algorithms,
with a useful perspective that can be brought to bear in these other
areas. I will also talk a bit about the relation of theory and
practice in machine learning, and describe some current important
issues in the practice of machine learning where theoretical work may
be able to have substantial impact. Slides for this tutorial are
available on the web at http://www.cs.cmu.edu/~avrim/Talks/FOCS03/.