Stochastic Refinement

The research presented in this paper is motivated by the following question. How can the generality order of clauses and the relevant concepts such as refinement be adapted to be used in a stochastic search? To address this question we introduce the concept of stochastic refinement operators and adapt a framework, called stochastic refinement search. In this paper we introduce stochastic refinements of a clause as a probability distribution over a set of clauses. This probability distribution can be viewed as a prior in a stochastic ILP search. We study the properties of a stochastic refinement search as two well known Markovian approaches: 1) Gibbs sampling algorithm and 2) random heuristic search. As a Gibbs sampling algorithm, a stochastic refinement search iteratively generates random samples from the hypothesis space according to a posterior distribution. We show that a minimum sample size can be set so that in each iteration a consistent clause is generated with a high probability. We study the stochastic refinement operators within the framework of random heuristic search and use this framework to characterise stochastic search methods in some ILP systems. We also study a special case of stochastic refinement search where refinement operators are defined with respect to subsumption order relative to a bottom clause. This paper also provided some insights to explain the relative advantages of using stochastic lgg-like operators as in the ILP systems Golem and ProGolem.