[Colloquium] Banerjee talk - 12/4 12:15 at TTI
Meridel Trimble
mtrimble at tti-c.org
Tue Dec 2 09:10:18 CST 2003
TOYOTA TECHNOLOGICAL INSTITUTE TALK
Speaker: Arindam Banerjee
Laboratory for Artificial Neural Systems (LANS), University of Texas
Speakers 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
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