Automated Refinement of First-Order Horn-Clause Domain Theories
Machine Learning
Revision of first-order Bayesian classifiers
ILP'02 Proceedings of the 12th international conference on Inductive logic programming
Probabilistic first-order theory revision from examples
ILP'05 Proceedings of the 15th international conference on Inductive Logic Programming
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Recently, there has been great interest in integrating first-order logic based formalisms with mechanisms for probabilistic reasoning, thus defining probabilistic first-order theories (PFOT).Several algorithms for learning PFOTs have been proposed in the literature. They all learn the model from scratch. Consider a PFOT approximately correct, i.e., such that only a few points of its structure prevent it from reflecting the database correctly. It is much more efficient to identify these points and then propose modifications only to them than to use an algorithm that learns the theory from scratch. Therefore, in [3] we proposed a Bayesian Logic Programs Revision system (RBLP), which receives an initial BLP and through the examples discovers points that fail in covering some of them, similarly to FORTE [4] for the logical approach. These points are called logical revision points. RBLP then considers modifications only for those points choosing the best one through a scoring function. It is required that the implemented modification improves examples covering. It is expected that the returned BLP is consistent with the database.When learning or revising probabilistic first-order theories negative examples are incorporated into the set of positive examples, since the distributions of probabilities will reflect this difference in accordance with the domain of the predicates. At first, this would suggest only using generalization operators. The probabilistic learning algorithms also considers specialization operators where specialization is guided by the scoring function. The question arises of whether using specialization operators when revising a PFOT can improve classification and the result of the scoring function.In [2], besides experimentally comparing scoring functions, we extended RBLP, presenting PFORTE, arguing for the use of specialization operators even when there are no negative examples. We defined then probabilistic revision points, which are the places in theory that result in inaccurate classification of examples (the example was proved, but the value infered for the class is not the one given in the example). Modifications in these points are proposed by specialization operators and the best one is chosen through a scoring function. It is required that these modifications improve the score while not allowing any example to be unproved.Although the ideas presented here can be used for most kinds of PFOTs, we used BLP [1] to implement our system and experimentally compare the results.In the present work, we further study the benefits of considering specialization operators. We compare PFORTE, RBLP, and RBLP modified to allow specialization when a rule is being created by the add rule operator, using four datasets and considering conditional log likelihood as scoring function (since it obtained in [2] the best results). The resultant probabilistic accuracy for PFORTE was the best one considering p family domain, we provide to PFORTE an approximately correct PFOT (85% of covering and 78% of classification) and an empty PFOT. The running time average for theory revision was 2,92 times faster than for learning from scratch. The experiment suggests that it may be more efficient revising than learning from scratch when the PFOT is approximately correct.