Sparse Linear Isotonic Models

TL;DR

This paper introduces Sparse Linear Isotonic Models (SLIMs) that combine sparse linear models with additive isotonic models to effectively handle high-dimensional data, providing accurate parameter estimation under mild assumptions.

Contribution

The paper proposes a novel high-dimensional model, SLIMs, and a two-step estimation algorithm that jointly estimates sparse parameters and monotone functions, advancing additive isotonic modeling.

Findings

The algorithm accurately estimates parameters under mild assumptions.

Preliminary experiments support the theoretical guarantees.

SLIMs outperform traditional models in high-dimensional settings.

Abstract

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predictors; in particular, additive isotonic models (AIMs) assume the unknown transformations to be monotone. In this paper, we introduce sparse linear isotonic models (SLIMs) for highdimensional problems by hybridizing ideas in parametric sparse linear models and AIMs, which enjoy a few appealing advantages over both. In the high-dimensional setting, a two-step algorithm is proposed for estimating the sparse parameters as well as the monotone functions over predictors. Under mild statistical assumptions, we show that the algorithm can accurately estimate the parameters. Promising preliminary experiments are presented to support the theoretical results.