English

Regression for sets of polynomial equations

Machine Learning 2013-11-05 v4

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.

Keywords

Cite

@article{arxiv.1110.4531,
  title  = {Regression for sets of polynomial equations},
  author = {Franz Johannes Király and Paul von Bünau and Jan Saputra Müller and Duncan Blythe and Frank Meinecke and Klaus-Robert Müller},
  journal= {arXiv preprint arXiv:1110.4531},
  year   = {2013}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1108.1483

R2 v1 2026-06-21T19:23:17.279Z