Exhaustive Symbolic Regression (or how to find the best function for your data)

Abstract: Symbolic regression aims to find optimal functional representation of datasets, with broad applications across science. This is traditionally done using a "genetic algorithm" which stochastically searches function space using an evolution-inspired method for generating new trial functions. Motivated by the uncertainties inherent in this approach -- and its failure on seemingly simple test cases -- I will describe a new method which exhaustively searches and evaluates function space. Coupled to a model selection principle based on minimum description length, Exhaustive Symbolic Regression is guaranteed to find the simple equations that optimally balance simplicity with accuracy on any dataset. I will describe how the method works and showcase it on Hubble rate measurements and dynamical galaxy data.

Based on work with Deaglan Bartlett and Pedro G. Ferreira:
arxiv.org/abs/2211.11461
arxiv.org/abs/2301.04368

data structures and algorithmsmachine learningmathematical physicsinformation theoryoptimization and controldata analysis, statistics and probability

Audience: researchers in the topic

Mathematics, Physics and Machine Learning (IST, Lisbon)

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