Comparing optimistic and pessimistic constraint evaluation in shape-constrained symbolic regression

Christian Haider, Fabrício Olivetti De França, Gabriel Kronberger, Bogdan Burlacu

Research output: Chapter in Book/Report/Conference proceedingsConference contributionpeer-review

Abstract

Shape-constrained Symbolic Regression integrates prior knowledge about the function shape into the symbolic regression model. This can be used to enforce that the model has desired properties such as monotonicity, or convexity, among others. Shape-constrained Symbolic Regression can also help to create models with better extrapolation behavior and reduced sensitivity to noise. The constraint evaluation can be challenging because exact evaluation of constraints may require a search for the extrema of non-convex functions. Approximations via interval arithmetic allow to efficiently find bounds for the extrema of functions. However, interval arithmetic can lead to overly wide bounds and therefore produces a pessimistic estimation. Another possibility is to use sampling which underestimates the true range. Sampling therefore produces an optimistic estimation. In this paper we evaluate both methods and compare them on different problem instances. In particular we evaluate the sensitivity to noise and the extrapolation capabilities in combination with noise data. The results indicate that the optimistic approach works better for predicting out-of-domain points (extrapolation) and the pessimistic approach works better for high noise levels.

Original languageEnglish
Title of host publicationGECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference
PublisherAssociation for Computing Machinery, Inc
Pages938-945
Number of pages8
ISBN (Electronic)9781450392372
DOIs
Publication statusPublished - 8 Jul 2022
Event2022 Genetic and Evolutionary Computation Conference, GECCO 2022 - Virtual, Online, United States
Duration: 9 Jul 202213 Jul 2022

Publication series

NameGECCO 2022 - Proceedings of the 2022 Genetic and Evolutionary Computation Conference

Conference

Conference2022 Genetic and Evolutionary Computation Conference, GECCO 2022
Country/TerritoryUnited States
CityVirtual, Online
Period09.07.202213.07.2022

Keywords

  • prior knowledge
  • shape constraints
  • symbolic regression

Fingerprint

Dive into the research topics of 'Comparing optimistic and pessimistic constraint evaluation in shape-constrained symbolic regression'. Together they form a unique fingerprint.

Cite this