LASSO ISOtone for High Dimensional Additive Isotonic Regression

TL;DR

This paper introduces LASSO Isotone (LISO), a new method for high-dimensional additive isotonic regression that combines sparse modeling with monotonicity constraints, enabling variable selection and efficient computation.

Contribution

The paper proposes LISO, a novel approach integrating LASSO-like sparsity with additive isotonic regression, including an algorithm and convergence analysis for high-dimensional data.

Findings

LISO effectively performs variable selection in high-dimensional settings.

The algorithm converges numerically under certain conditions.

Simulations demonstrate the method's accuracy and efficiency.

Abstract

Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear modelling to additive isotonic regression. Thus, it is viable in many situations with high dimensional predictor variables, where selection of significant versus insignificant variables are required. We suggest an algorithm involving a modification of the backfitting algorithm CPAV. We give a numerical convergence result, and finally examine some of its properties through simulations. We also suggest some possible extensions that improve performance, and allow calculation to be carried out when the direction of the monotonicity is unknown.