An Exact Approach to Learning Probabilistic Relational Model

Probabilistic Graphical Models (PGMs) offer a popular framework including a variety of statistical formalisms, such as Bayesian networks (BNs). These latter are able to depict real-world situations with high degree of uncertainty. Due to their power and flexibility, several extensions were proposed, ensuring thereby the suitability of their use. Probabilistic Relational Models (PRMs) extend BNs to work with relational databases rather than propositional data. Their construction represents an active area since it remains the most complicated issue. Only few works have been proposed in this direction, and most of them don’t guarantee an optimal identification of their dependency structure. In this paper we intend to propose an approach that ensures returning an optimal PRM structure. It is inspired from a BN method whose performance was already proven.

[1]  P. P. Chakrabarti,et al.  AWA* - A Window Constrained Anytime Heuristic Search Algorithm , 2007, IJCAI.

[2]  Brandon M. Malone.  Learning optimal Bayesian networks with heuristic search , 2012 .

[3]  Qiang Ji,et al.  Efficient Structure Learning of Bayesian Networks using Constraints , 2011, J. Mach. Learn. Res..

[4]  Mouna Ben Ishak.  Probabilistic relational models : learning and evaluation : The relational Bayesian networks case , 2015 .

[5]  Andrew McCallum,et al.  Introduction to Statistical Relational Learning , 2007 .

[6]  Changhe Yuan,et al.  Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks , 2013, UAI.

[7]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[8]  Doug Fisher,et al.  Learning from Data: Artificial Intelligence and Statistics V , 1996 .

[9]  Brian J. Taylor,et al.  Learning Causal Models of Relational Domains , 2010, AAAI.

[10]  David Maxwell Chickering,et al.  Learning Bayesian Networks is NP-Complete , 2016, AISTATS.

[11]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[12]  Gregory F. Cooper,et al.  A Bayesian Method for the Induction of Probabilistic Networks from Data , 1992 .

[13]  Changhe Yuan,et al.  Learning Optimal Bayesian Networks: A Shortest Path Perspective , 2013, J. Artif. Intell. Res..

[14]  Daphne Koller,et al.  Probabilistic reasoning for complex systems , 1999 .

[15]  Changhe Yuan,et al.  Learning Optimal Bayesian Networks Using A* Search , 2011, IJCAI.

[16]  James Cussens,et al.  Bayesian network learning with cutting planes , 2011, UAI.

[17]  Xi Chen,et al.  Finding optimal control policy in Probabilistic Boolean Networks with hard constraints by using integer programming and dynamic programming , 2010, BIBM.

[18]  Avi Pfeffer,et al.  Probabilistic Frame-Based Systems , 1998, AAAI/IAAI.

[19]  Daphne Koller,et al.  Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks , 2005, UAI.

[20]  Ben Taskar,et al.  Learning Probabilistic Models of Relational Structure , 2001, ICML.