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 equations, from observed data and expert knowledge. Deterministic grammars, such context-free have been used to limit search spaces equation discovery by providing hard constraints specify which equations consider not. In this paper, we propose use probabilistic grammars discovery. Such encode soft constraints, specifying prior probability distribution on space possible equations. We show can be elegantly flexibly formulate parsimony principle, favors simpler through probabilities attached rules grammars. demonstrate probabilistic, rather than deterministic context Monte-Carlo algorithm for grammar-based leads more efficient Finally, distributions over spaces, foundations are laid Bayesian approaches