Learning Single Index Models in High Dimensions

TL;DR

This paper introduces three efficient algorithms for learning Single Index Models in high-dimensional settings, providing theoretical guarantees and empirical validation of their advantages over existing methods.

Contribution

The paper proposes novel high-dimensional algorithms for SIM inference, with theoretical risk bounds and empirical validation demonstrating improved performance.

Findings

Algorithms achieve lower excess risk compared to GLMs.

Methods are computationally efficient for high-dimensional data.

Experimental results show superior accuracy over low-dimensional SIM methods.

Abstract

Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights, and the nonlinear function. While methods have been described to learn SIMs in the low dimensional regime, a method that can efficiently learn SIMs in high dimensions has not been forthcoming. We propose three variants of a computationally and statistically efficient algorithm for SIM inference in high dimensions. We establish excess risk bounds for the proposed algorithms and experimentally validate the advantages that our SIM learning methods provide relative to Generalized Linear Model (GLM) and low dimensional SIM based learning methods.