Sparse Linear Isotonic Models

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 high-dimensional 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.