Projection-Based PILP: Computational Learning Theory with Empirical Results

Abstract

Evaluations of advantages of Probabilistic Inductive Logic Programming (PILP) against ILP have not been conducted from a computational learning theory point of view. We propose a PILP framework, projection-based PILP, in which surjective projection functions are used to produce a “lossy” compression dataset from an ILP dataset. We present sample complexity results including conditions when projection-based PILP needs fewer examples than PAC. We experimentally confirm the theoretical bounds for the projection-based PILP in the Blackjack domain using Cellist, a system which machine learns Probabilistic Logic Automata. In our experiments projection-based PILP shows lower predictive error than the theoretical bounds and achieves substantially lower predictive error than ILP. To the authors’ knowledge this is the first paper describing both a computer learning theory and related empirical results on an advantage of PILP against ILP.