Efficient generator of mathematical expressions for symbolic regression

Mežnar, Sebastian (avtor), Džeroski, Sašo (avtor), Todorovski, Ljupčo (avtor)

We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. It combines simple atomic units with shared weights to recursively encode and decode the individual nodes in the hierarchy. Encoding is performed bottom-up and decoding top-down. We empirically show that HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. The latter can be efficiently explored with various optimization methods to address the task of symbolic regression. Indeed, random search through the latent space of HVAE performs better than random search through expressions generated by manually crafted probabilistic grammars for mathematical expressions. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.

• Jezik: Angleški jezik
• Ključne besede: symbolic regression, equation discovery, generative models, variational autoencoders, evolutionary algorithms
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: Str. 4563-4596
• Številčenje: Vol. 112, iss. 11
• PID: 20.500.12556/RUL-153002
• UDK: 004.8
• ISSN pri članku: 1573-0565
• DOI: 10.1007/s10994-023-06400-2
• COBISS.SI-ID: 176785923
• Datum objave v RUL: 14.12.2023

Gradivo je del revije

• Naslov: Machine learning
• Skrajšan naslov: Mach. learn.
• Založnik: Springer Nature
• ISSN: 1573-0565
• COBISS.SI-ID: 513211417

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: simbolna regresija, odkrivanje enačb, generativni modeli, variacijski samokodirniki, evolucijski algoritmi