Overlapping Sliced Inverse Regression for Dimension Reduction

TL;DR

This paper introduces OSIR, an improved version of sliced inverse regression that uses overlapping slices to more accurately identify the effective dimension reduction space and the number of significant factors.

Contribution

The paper proposes the OSIR algorithm, which refines SIR with overlapping slices to better estimate the dimension reduction space and factor count, and proves its consistency.

Findings

OSIR outperforms traditional SIR in simulations and real data.

OSIR effectively captures information from derivatives of the inverse regression curve.

The algorithm is proven to be -consistent.

Abstract

Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose to refine the SIR algorithm through an overlapping slicing scheme. The new algorithm, called overlapping sliced inverse regression (OSIR), is able to estimate the effective dimension reduction space and determine the number of effective factors more accurately. We show that such overlapping procedure has the potential to identify the information contained in the derivatives of the inverse regression curve, which helps to explain the superiority of OSIR. We also prove that OSIR algorithm is $\sqrt n $-consistent and verify its effectiveness by simulations and real applications.