Efficient Sampling in Relational Feature Spaces

Abstract

State-of-the-art algorithms implementing the ‘extended transformation approach’ to propositionalization use backtrack depth first search for the construction of relational features (first order atom conjunctions) complying to user’s mode/type declarations and a few basic syntactic conditions. As such they incur a complexity factor exponential in the maximum allowed feature size. Here I present an alternative based on an efficient reduction of the feature construction problem on the propositional satisfiability (SAT) problem, such that the latter involves only Horn clauses and is therefore tractable: a model to a propositional Horn theory can be found without backtracking in time linear in the number of literals contained. This reduction allows to either efficiently enumerate the complete set of correct features (if their total number is polynomial in the maximum feature size), or otherwise efficiently obtain a random sample from the uniform distribution on the feature space. The proposed sampling method can also efficiently provide an unbiased estimate of the total number of correct features entailed by the user language declaration.