Sparse Partitioning: Nonlinear regression with binary or tertiary predictors, with application to association studies

TL;DR

Sparse Partitioning is a Bayesian regression method for identifying influential predictor groups in association studies, capable of handling binary or tertiary predictors and exceeding sample size, without restrictive assumptions.

Contribution

It introduces a novel Bayesian approach that explores high posterior probability partitions of predictors, accommodating complex predictor-response relationships without prior assumptions.

Findings

Performs well on simulated data, matching existing methods under their assumptions.

Outperforms traditional methods when assumptions are violated.

Effective for high-dimensional association studies.

Abstract

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or tertiary predictors and allows the number of predictors to exceed the size of the sample, two properties which make it well suited for association studies. Sparse Partitioning differs from other regression methods by placing no restrictions on how the predictors may influence the response. To compensate for this generality, Sparse Partitioning implements a novel way of exploring the model space. It searches for high posterior probability partitions of the predictor set, where each partition defines groups of predictors that jointly influence the response. The result is a robust method that requires no prior knowledge of the true predictor--response relationship. Testing on simulated data suggests Sparse Partitioning will typically match the performance of an existing method on a data set which obeys the existing method's model assumptions. When these assumptions are violated, Sparse Partitioning will generally offer superior performance.