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

Joshua W. Lambert, Gregory S. Hawk

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 (R2)) 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.

Original languageEnglish
Pages (from-to)277-284
Number of pages8
JournalInternational Journal of Data Science and Analytics
Issue number3
StatePublished - Sep 1 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


  • Feasible solution
  • Multiple
  • Objective
  • Optimal
  • Pareto
  • Regression
  • Subset selection

ASJC Scopus subject areas

  • Information Systems
  • Modeling and Simulation
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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