Using Shape Constraints for Improving Symbolic Regression Models

• URL: http://arxiv.org/abs/2107.09458v1
• Date: Tue, 20 Jul 2021 12:53:28 GMT
• Title: Using Shape Constraints for Improving Symbolic Regression Models
• Authors: Christian Haider, Fabricio Olivetti de Fran\c{c}a, Bogdan Burlacu, Gabriel Kronberger
• Abstract summary: We describe and analyze algorithms for shape-constrained symbolic regression. We use a set of models from physics textbooks to test the algorithms. The results show that all algorithms are able to find models which conform to all shape constraints.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever a data-driven model obtained from measurements must have certain properties (e.g. positivity, monotonicity or convexity/concavity). We implement shape constraints using a soft-penalty approach which uses multi-objective algorithms to minimize constraint violations and training error. We use the non-dominated sorting genetic algorithm (NSGA-II) as well as the multi-objective evolutionary algorithm based on decomposition (MOEA/D). We use a set of models from physics textbooks to test the algorithms and compare against earlier results with single-objective algorithms. The results show that all algorithms are able to find models which conform to all shape constraints. Using shape constraints helps to improve extrapolation behavior of the models.

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