published: Feb. 25, 2007, recorded: May 2005, views: 5599
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
This tutorial will focus on entropy, exponential families, and information projection. We'll start by seeing the sense in which entropy is the only reasonable definition of randomness. We will then use entropy to motivate exponential families of distributions — which include the ubiquitous Gaussian, Poisson, and Binomial distributions, but also very general graphical models. The task of fitting such a distribution to data is a convex optimization problem with a geometric interpretation as an "information projection": the projection of a prior distribution onto a linear subspace (defined by the data) so as to minimize a particular information-theoretic distance measure. This projection operation, which is more familiar in other guises, is a core optimization task in machine learning and statistics. We'll study the geometry of this problem and discuss two popular iterative algorithms for it.
Download slides: geometry.ppt (1.7 MB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !