Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations
<|reference_start|>Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations: Symbolic regression has excelled in uncovering equations from physics, chemistry, biology, and related disciplines. However, its effectiveness becomes less certain when applied to experimental data lacking inherent closed-form expressions. Empirically derived relationships, such as entire stress-strain curves, may defy concise closed-form representation, compelling us to explore more adaptive modeling approaches that balance flexibility with interpretability. In our pursuit, we turn to Generalized Additive Models (GAMs), a widely used class of models known for their versatility across various domains. Although GAMs can capture non-linear relationships between variables and targets, they cannot capture intricate feature interactions. In this work, we investigate both of these challenges and propose a novel class of models, Shape Arithmetic Expressions (SHAREs), that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. SHAREs also provide a unifying framework for both of these approaches. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints based on the model's size.<|reference_end|>
@article{kacprzyk2024shape,
    title={Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond
  Closed-Form Equations},
    author={Krzysztof Kacprzyk, Mihaela van der Schaar},
    journal={arXiv preprint arXiv:2404.09788},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.09788},
    primaryClass={cs.LG stat.ML}
}