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

Krzysztof Kacprzyk, Mihaela van der Schaar
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3601-3609, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-kacprzyk24a, title = { Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations }, author = {Kacprzyk, Krzysztof and van der Schaar, Mihaela}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3601--3609}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/kacprzyk24a/kacprzyk24a.pdf}, url = {https://proceedings.mlr.press/v238/kacprzyk24a.html}, 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. } }
Endnote
%0 Conference Paper %T Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations %A Krzysztof Kacprzyk %A Mihaela van der Schaar %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-kacprzyk24a %I PMLR %P 3601--3609 %U https://proceedings.mlr.press/v238/kacprzyk24a.html %V 238 %X 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.
APA
Kacprzyk, K. & van der Schaar, M.. (2024). Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3601-3609 Available from https://proceedings.mlr.press/v238/kacprzyk24a.html.

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