Generalized Fixed-Depth Prefix and Postfix Symbolic Regression Grammars
<|reference_start|>Generalized Fixed-Depth Prefix and Postfix Symbolic Regression Grammars: 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.<|reference_end|>
@article{finkelstein2024generalized,
    title={Generalized Fixed-Depth Prefix and Postfix Symbolic Regression Grammars},
    author={Edward Finkelstein},
    journal={arXiv preprint arXiv:2410.08137},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.08137},
    primaryClass={cs.SC}
}