Branch and Bound to Assess Stability of Regression Coefficients in Uncertain Models

TL;DR

This paper introduces a branch and bound algorithm to efficiently evaluate the stability of regression coefficients across various high-dimensional models, aiding interpretation in uncertain modeling scenarios.

Contribution

It presents a novel algorithm and mathematical framework for assessing coefficient stability in high-dimensional, uncertain regression models.

Findings

Efficient search for coefficient bounds using branch and bound.

Mathematical results supporting the algorithm.

Practical application demonstrated with code link.

Abstract

It can be difficult to interpret a coefficient of an uncertain model. A slope coefficient of a regression model may change as covariates are added or removed from the model. In the context of high-dimensional data, there are too many model extensions to check. However, as we show here, it is possible to efficiently search, with a branch and bound algorithm, for maximum and minimum values of that adjusted slope coefficient over a discrete space of regularized regression models. Here we introduce our algorithm, along with supporting mathematical results, an example application, and a link to our computer code, to help researchers summarize high-dimensional data and assess the stability of regression coefficients in uncertain models.