Inverse regression for ridge recovery II: Numerics
For researchers in sufficient dimension reduction, this is an incremental numerical analysis of existing methods for ridge recovery.
The paper explores numerical subtleties of using sliced inverse regression (SIR) and sliced average variance estimation (SAVE) for ridge recovery in noiseless data, providing eigenvalue analysis and demonstrating on test problems.
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.