Parameter Estimation in Stochastic Logic Programs

Abstract

Stochastic logic programs (SLPs) are logic programs with parameterised clauses which define a log-linear distribution over refutations of goals. The log-linear distribution provides, by marginalisation, a distribution over variable bindings, allowing SLPs to compactly represent quite complex distributions. We analyse the fundamental statistical properties of SLPs addressing issues concerning infinite derivations, 'unnormalised’ SLPs and impure SLPs. After detailing existing approaches to parameter estimation for log-linear models and their application to SLPs, we present a new algorithm called failure-adjusted maximisation (FAM) . FAM is an instance of the EM algorithm that applies specifically to normalised SLPs and provides a closed-form for computing parameter updates within an iterative maximisation approach. We empirically show that FAM works on some small examples and discuss methods for applying it to bigger problems.