PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Kernel Methods for Missing Variables
Alex Smola, S V N Vishwanathan and Thomas Hoffman
In: AISTATS 2005, 06 - 08 Jan 2005, Barbados.

Abstract

We present methods for dealing with missing variables in the context of Gaussian Processes and Support Vector Machines. This solves an important problem which has largely been ignored by kernel methods: How to systematically deal with incomplete data? Our method can also be applied to problems with partially observed labels as well as to the transductive setting where we view the labels as missing data. Our approach relies on casting kernel methods as an estimation problem in exponential families. Hence, estimation with missing variables becomes a problem of computing marginal distributions, and finding efficient optimization methods. To that extent we propose an optimization scheme which extends the Concave Convex Procedure (CCP) of Yuille and Rangarajan, and present a simplified and intuitive proof of its convergence. We show how our algorithm can be specialized to various cases in order to efficiently solve the optimization problems that arise. Encouraging preliminary experimental results on the USPS dataset are also presented.

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EPrint Type:Conference or Workshop Item (Oral)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2053
Deposited By:S V N Vishwanathan
Deposited On:16 January 2006