Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication

• URL: http://arxiv.org/abs/2109.13895v1
• Date: Tue, 28 Sep 2021 17:47:51 GMT
• Title: Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication
• Authors: Lukas Kammerer, Gabriel Kronberger, Bogdan Burlacu, Stephan M. Winkler, Michael Kommenda, Michael Affenzeller
• Abstract summary: Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions.
• Score: 2.055204980188575
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness, trustworthiness and plausibility, that are not easily achievable using standard approaches like genetic programming for symbolic regression. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. The algorithm uses a context-free grammar to produce models that are parameterized by a non-linear least squares local optimization procedure. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions. Enumeration order is established via heuristics designed to improve search efficiency. Empirical tests on a comprehensive benchmark suite show that our approach is competitive with genetic programming in many noiseless problems while maintaining desirable properties such as simple, reliable models and reproducibility.

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