Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations

• URL: http://arxiv.org/abs/2404.09788v1
• Date: Mon, 15 Apr 2024 13:44:01 GMT
• Title: Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations
• Authors: Krzysztof Kacprzyk, Mihaela van der Schaar,
• Abstract summary: Generalized Additive Models (GAMs) can capture non-linear relationships between variables and targets, but they cannot capture intricate feature interactions. We propose Shape Expressions Arithmetic ( SHAREs) that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints.
• Score: 56.78271181959529
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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