Complexity Measures for Multi-Objective Symbolic Regression

Michael Kommenda; Andreas Beham; Michael Affenzeller; Gabriel Kronberger

doi:10.1007/978-3-319-27340-2_51

Complexity Measures for Multi-Objective Symbolic Regression

Michael Kommenda, Andreas Beham, Michael Affenzeller, Gabriel Kronberger

Institute of Formal Models and Verification

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity. In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi-objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.

Original language	English
Title of host publication	Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers
Editors	R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia
Publisher	Springer
Pages	409-416
Number of pages	8
Volume	9520
ISBN (Print)	978-3-319-27339-6
DOIs	https://doi.org/10.1007/978-3-319-27340-2_51
Publication status	Published - 2015

Publication series

Name	Lecture Notes in Computer Science (LNCS)
ISSN (Print)	0302-9743

Fields of science

102 Computer Sciences
603109 Logic
202006 Computer hardware

JKU Focus areas

Computation in Informatics and Mathematics

Access to Document

10.1007/978-3-319-27340-2_51

Cite this

Kommenda, M., Beham, A., Affenzeller, M., & Kronberger, G. (2015). Complexity Measures for Multi-Objective Symbolic Regression. In R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia (Ed.), Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers (Vol. 9520, pp. 409-416). (Lecture Notes in Computer Science (LNCS)). Springer. https://doi.org/10.1007/978-3-319-27340-2_51

Kommenda, Michael ; Beham, Andreas ; Affenzeller, Michael et al. / Complexity Measures for Multi-Objective Symbolic Regression. Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers. editor / R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia. Vol. 9520 Springer, 2015. pp. 409-416 (Lecture Notes in Computer Science (LNCS)).

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abstract = "Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity. In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi-objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.",

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Kommenda, M, Beham, A, Affenzeller, M & Kronberger, G 2015, Complexity Measures for Multi-Objective Symbolic Regression. in R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia (ed.), Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers. vol. 9520, Lecture Notes in Computer Science (LNCS), Springer, pp. 409-416. https://doi.org/10.1007/978-3-319-27340-2_51

Complexity Measures for Multi-Objective Symbolic Regression. / Kommenda, Michael; Beham, Andreas; Affenzeller, Michael et al.
Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers. ed. / R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia. Vol. 9520 Springer, 2015. p. 409-416 (Lecture Notes in Computer Science (LNCS)).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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Kommenda M, Beham A, Affenzeller M, Kronberger G. Complexity Measures for Multi-Objective Symbolic Regression. In R. Moreno-Diaz, F.Pichler, A. Quesada-Arencibia, editor, Computer Aided Systems Theory – EUROCAST 2015. 15th International Conference, Las Palmas de Gran Canaria, Spain, February 8-13, 2015, Revised Selected Papers. Vol. 9520. Springer. 2015. p. 409-416. (Lecture Notes in Computer Science (LNCS)). doi: 10.1007/978-3-319-27340-2_51