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

TL;DR

This paper presents a deterministic symbolic regression algorithm that uses syntactical constraints and semantic deduplication to efficiently explore model spaces, achieving competitive results with genetic programming while ensuring interpretability and reproducibility.

Contribution

The proposed method introduces a structured, deterministic approach to symbolic regression that reduces search space and enhances model quality compared to traditional stochastic methods.

Findings

Competitive performance on noiseless benchmarks

Produces simple, interpretable models

Ensures reproducibility and reliability

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.