[Colloquium] Banerjee talk today 12:15 at TTI

[Meridel Trimble]

TOYOTA TECHNOLOGICAL INSTITUTE TALK 

Speaker: Arindam Banerjee 
Laboratory for Artificial Neural Systems (LANS), University of Texas 
Speaker’s homepage: http://www.lans.ece.utexas.edu/~abanerjee/ 

Time: 12:15pm 
Date: Thursday, December. 4th, 2003 
Place: TTI-C (1427 East 60th Street, Second Floor - Press Building) 
*FREE LUNCH PROVIDED* 

Title: Optimal Bregman Prediction and its Applications to Clustering 

Abstract: Several techniques in prediction, clustering, approximation, etc., 
rely on the properties of the squared Euclidean distance. In this talk, with 
the help of convex analysis, we argue that some of the well known results 
actually hold good for a much larger class of distances called Bregman loss 
functions (BLFs). First, we generalize a well known result in probability 
theory that says that in the least square sense the conditional expectation is 
the optimal predictor of a random variable in a sub-sigma-algebra.  We show 
that the conditional expectation is optimal for all BLFs. Next, we introduce 
the concept of Bregman information. We propose and prove Jensen's equality to 
demonstrate its utility. Finally, we show applications of these results to 
hard and soft clustering. In the process, we establish a bijection between 
BLFs and exponential family distributions. 

If you have questions, or would like to meet the speaker, please contact 
Meridel at: 4-9873 or mtrimble at tti-c.org 

For information on future TTI-C talks or events, please go to the TTI-C Events 
page: http://www.tti-c.org/events.shtml