Phase transitions and stochastic local search in k-term DNF learning

Abstract

In the past decade, there has been a lot of interest in phase transitions within artificial intelligence, and more recently, in machine learning and inductive logic programming. We investigate phase transitions in learning k-term DNF boolean formulae, a practically relevant class of concepts. We do not only show that there exist phase transitions, but also characterize and locate these phase transitions using the parameters k, the number of positive and negative examples, and the number of boolean variables. Subsequently, we investigate stochastic local search (SLS) for k-term DNF learning. We compare several variants that first reduce k-term DNF to SAT and then apply well-known SLS algorithms, such as GSAT and WalkSAT. Our experiments indicate that WalkSAT is able to solve the largest fraction of hard problem instances.