Inverse regression for ridge recovery II: Numerics

TL;DR

This paper examines the numerical aspects of applying inverse regression methods, specifically SIR and SAVE, for ridge recovery in noiseless deterministic functions, providing detailed eigenvalue analysis and practical demonstrations.

Contribution

It offers a detailed numerical analysis of SIR and SAVE methods for ridge recovery, highlighting subtleties and demonstrating their effectiveness on test problems.

Findings

Eigenvalue analysis reveals key properties of the methods.

SIR and SAVE successfully recover ridge subspaces in tests.

Numerical subtleties impact the accuracy of ridge recovery.

Abstract

We investigate the application of sufficient dimension reduction (SDR) to a noiseless data set derived from a deterministic function of several variables. In this context, SDR provides a framework for ridge recovery. In this second part, we explore the numerical subtleties associated with using two inverse regression methods---sliced inverse regression (SIR) and sliced average variance estimation (SAVE)---for ridge recovery. This includes a detailed numerical analysis of the eigenvalues of the resulting matrices and the subspaces spanned by their columns. After this analysis, we demonstrate the methods on several numerical test problems.