Bayesian Machine Scientist

Introduction

Symbolic regression (SR) refers to a class of algorithms that search for interpretable symbolic expressions which capture relationships within data. More specifically, SR attempts to find compositions of simple functions that accurately map independent variables to dependent variables within a given dataset. SR was traditionally tackled through genetic programming, wherein evolutionary algorithms mutated and crossbred equations billions of times in search of the best match. There are problems with genetic programming, however, which stem from its inherent search constraints as well as its reliance upon heuristics and domain knowledge to balance goodness of fit and model complexity. To address these problems, Guimerà et. al (2020) proposed a Bayesian Machine Scientist (BMS), which combines i) a Bayesian approach that specifies informed priors over expressions and computes their respective posterior probabilities given the data at hand, and ii) a Markov chain Monte Carlo (MCMC) algorithm that samples from the posterior over expressions to more effectively explore the space of possible symbolic expressions.

AutoRA provides an adapted version of BMS for automating the discovery of interpretable models of human information processing.

References

R. Guimerà et al., A Bayesian machine scientist to aid in the solution of challenging scientific problems. Sci. Adv. 6, eaav697 (2020).