Identifying Pareto-based solutions for regression subset selection via a feasible solution algorithm

摘要

The concept of Pareto optimality has been utilized in fields such as engineering and economics to understand fluid dynamics and consumer behavior. In machine learning contexts, Pareto-optimality has been used to identify tuning parameters that best optimize a set of m criteria (multi-objective optimization). During the process of regression model selection, data scientists are often concerned with choosing a model which has the best single criterion (e.g., Akaike information criterion (AIC) or R-squared (R~2)) before continuing to check a number of other regression model characteristics (e.g., model size, form, diagnostics, and interpretability). This strategy is multi-objective in nature but single objective in its numeric execution. This paper will first introduce a feasible solution algorithm (FSA) and explain how it can be applied to multi-objective problems for regression subset selection. Then we introduce the general framework of Pareto optimality within the regression setting. We then apply the algorithm in a simulation setting where we seek to estimate the first four Pareto boundaries for regression models using two model fit criteria. Finally, we present an application where we use a US communities and crime dataset.