Generalized Fixed-Depth Prefix and Postfix Symbolic Regression Grammars

TL;DR

This paper introduces fixed-depth prefix and postfix symbolic regression grammars that can generate any expression, and compares their performance across various heuristic search strategies to improve efficiency in scientific discovery.

Contribution

It presents faultless fixed-depth grammars for prefix and postfix symbolic regression and analyzes their performance across multiple heuristic algorithms.

Findings

Performance varies with expression tree depth and grammar type.

Prefix and postfix grammars show different efficiencies depending on the expression.

The approach can accelerate the discovery of mathematical models.

Abstract

We develop faultless, fixed-depth, string-based, prefix and postfix symbolic regression grammars, capable of producing \emph{any} expression from a set of operands, unary operators and/or binary operators. Using these grammars, we outline simplified forms of 5 popular heuristic search strategies: Brute Force Search, Monte Carlo Tree Search, Particle Swarm Optimization, Genetic Programming, and Simulated Annealing. For each algorithm, we compare the relative performance of prefix vs postfix for ten ground-truth expressions implemented entirely within a common C++/Eigen framework. Our experiments show a comparatively strong correlation between the average number of nodes per layer of the ground truth expression tree and the relative performance of prefix vs postfix. The fixed-depth grammars developed herein can enhance scientific discovery by increasing the efficiency of symbolic regression, enabling faster identification of accurate mathematical models across various disciplines.