  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.
