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

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.