Probabilistic grammars for equation discovery

Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, such as context-free grammars, have been used to limit the search spaces in equation discovery by providing hard constraints that specify which equations to consider and which not. In this paper, we propose the use of probabilistic context-free grammars in equation discovery. Such grammars encode soft constraints, specifying a prior probability distribution on the space of possible equations. We show that probabilistic grammars can be used to elegantly and flexibly formulate the parsimony principle, that favors simpler equations, through probabilities attached to the rules in the grammars. We demonstrate that the use of probabilistic, rather than deterministic grammars, in the context of a Monte-Carlo algorithm for grammar-based equation discovery, leads to more efficient equation discovery. Finally, by specifying prior probability distributions over equation spaces, the foundations are laid for Bayesian approaches to equation discovery. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This paper proposes the use of probabilistic context-free grammars in equation discovery, encoding soft constraints to specify a prior probability distribution on the space of possible equations. It demonstrates that this approach is more efficient than using deterministic grammars in the context of equation discovery, and lays the foundations for Bayesian approaches to equation discovery by specifying prior probability distributions over equation spaces.