Compressing probabilistic Prolog programs

Abstract ProbLog is a recently introduced probabilistic extension of Prolog (De Raedt, et al. in Proceedings of the 20th international joint conference on artificial intelligence, pp. 2468–2473, 2007). A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is then defined by the success probability of a query in a randomly sampled program. This paper introduces the theory compression task for ProbLog, which consists of selecting that subset of clauses of a given ProbLog program that maximizes the likelihood w.r.t. a set of positive and negative examples. Experiments in the context of discovering links in real biological networks demonstrate the practical applicability of the approach.

[1]  Luc De Raedt,et al.  Probabilistic logic learning , 2003, SKDD.

[2]  David Poole,et al.  Logic programming, abduction and probability , 1993, New Generation Computing.

[3]  Yoshitaka Kameya,et al.  Parameter Learning of Logic Programs for Symbolic-Statistical Modeling , 2001, J. Artif. Intell. Res..

[4]  S. Wrobel.  First Order Theory Reenement , 1996 .

[5]  Hannu Toivonen,et al.  Link Discovery in Graphs Derived from Biological Databases , 2006, DILS.

[6]  Ken Satoh,et al.  Compiling Bayesian Networks by Symbolic Probability Calculation Based on Zero-Suppressed BDDs , 2007, IJCAI.

[7]  David Poole,et al.  Probabilistic Horn Abduction and Bayesian Networks , 1993, Artif. Intell..

[8]  S. Muggleton.  Stochastic Logic Programs , 1996 .

[9]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.

[10]  P. Bork,et al.  Association of genes to genetically inherited diseases using data mining , 2002, Nature Genetics.

[11]  De Raedt,et al.  Advances in Inductive Logic Programming , 1996 .

[12]  Raymond J. Mooney,et al.  Inducing Deterministic Prolog Parsers from Treebanks: A Machine Learning Approach , 1994, AAAI.

[13]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[14]  Ronen Feldman,et al.  Bias-Driven Revision of Logical Domain Theories , 1993, J. Artif. Intell. Res..

[15]  Peter A. Flach.  Simply logical - intelligent reasoning by example , 1994, Wiley professional computing.

[16]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[17]  Adnan Darwiche,et al.  Compiling Bayesian Networks Using Variable Elimination , 2007, IJCAI.

[18]  Norbert Fuhr,et al.  Probabilistic datalog: Implementing logical information retrieval for advanced applications , 2000, J. Am. Soc. Inf. Sci..