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  Matrix Exponential Gradient Updates for On-line Learning and Bregman Projection

Tsuda, K., Rätsch, G., & Warmuth, M. (2005). Matrix Exponential Gradient Updates for On-line Learning and Bregman Projection. In L. Saul, Y. Weiss, & L. Bottou (Eds.), Advances in Neural Information Processing Systems 17 (pp. 1425-1432). Cambridge, MA, USA: MIT Press.

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 Creators:
Tsuda, K1, 2, Author              
Rätsch, G1, 2, Author              
Warmuth, MK, Author
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements.

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 Dates: 2005-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 2859
 Degree: -

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Title: Eighteenth Annual Conference on Neural Information Processing Systems (NIPS 2004)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2004-12-13 - 2004-12-16

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Title: Advances in Neural Information Processing Systems 17
Source Genre: Proceedings
 Creator(s):
Saul, LK, Editor
Weiss, Y, Editor
Bottou, L, Editor
Affiliations:
-
Publ. Info: Cambridge, MA, USA : MIT Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1425 - 1432 Identifier: ISBN: 0-262-19534-8