PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Regression for sets of polynomial equations
F J Kiraly, Paul Buenau, J S Müller, D A J Blythe, Frank Meinecke and Klaus-Robert Müller
In: AISTATS 2012, 21-23 April 2012, La Palma, Canary Islands La Palma, Canary Islands La Palma, Canary Islands.

Abstract

We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimization. Ideal regression is useful whenever the solution to a learning problem can be described by a system of polynomial equations. As an example, we demonstrate how to formulate Stationary Subspace Analysis (SSA), a source separation problem, in terms of ideal regression, which also yields a consistent estimator for SSA. We then compare this estimator in simulations with previous optimization-based approaches for SSA

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EPrint Type:Conference or Workshop Item (Talk)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:9467
Deposited By:Paul Buenau
Deposited On:16 March 2012