ABSTRACT
Intelligent agents must be able to handle the complexity and uncertainty of the real world. Logical AI has focused mainly on the former, and statistical AI on the latter. Markov logic combines the two by attaching weights to first-order formulas and viewing them as templates for features of Markov networks. Inference algorithms for Markov logic draw on ideas from satisfiability, Markov chain Monte Carlo and knowledge-based model construction. Learning algorithms are based on the voted perceptron, pseudo-likelihood and inductive logic programming. Markov logic has been successfully applied to a wide variety of problems in natural language understanding, vision, computational biology, social networks and others, and is the basis of the open-source Alchemy system.
- J. Besag. Statistical analysis of non-lattice data. The Statistician, 24: 179--195, 1975.Google ScholarCross Ref
- H. Bui, T. Huynh, and R. de Salvo Braz. Exact lifted inference with distinct soft evidence on every object. In Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, 2012. Google ScholarDigital Library
- H. Bui, T. Huynh, and D. Sontag. Lifted tree-reweighted variational inference. In Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 2014.Google ScholarDigital Library
- M. Collins. Discriminative training methods for hidden Markov models: Theory and experiments with perceptron algorithms. In Proceedings of the 2002 Conference on Empirical Methods in Natural Language Processing, pages 1--8, Philadelphia, PA, 2002. ACL. Google ScholarDigital Library
- M. Craven and S. Slattery. Relational learning with statistical predicate invention: Better models for hypertext. Machine Learning, 43(1/2): 97--119, 2001.Google ScholarDigital Library
- P. Damien, J. Wakefield, and S. Walker. Gibbs sampling for Bayesian non-conjugate and hierarchical models by auxiliary variables. Journal of the Royal Statistical Society, Series B, 61:331--344, 1999.Google ScholarCross Ref
- L. De Raedt and L. Dehaspe. Clausal discovery. Machine Learning, 26: 99--146, 1997. Google ScholarDigital Library
- G. V. den Broeck and A. Darwiche. On the complexity and approximation of binary evidence in lifted inference. In Advances in Neural Information Processing Systems 26, pages 2868--2876, 2013. Google ScholarDigital Library
- G. V. den Broeck and J. Davis. Conditioning in first-order knowledge compilation and lifted probabilistic inference. In Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. AAAI Press, 2012. Google ScholarDigital Library
- P. Domingos and D. Lowd. Markov Logic: An Interface Layer for AI. Morgan & Claypool, San Rafael, CA, 2009. Google ScholarDigital Library
- P. Domingos and M. Richardson. Mining the network value of customers. In Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 57--66, San Francisco, CA, 2001. ACM Press. Google ScholarDigital Library
- M. R. Genesereth and N. J. Nilsson. Logical Foundations of Artificial Intelligence. Morgan Kaufmann, San Mateo, CA, 1987. Google ScholarDigital Library
- W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors. Markov Chain Monte Carlo in Practice. Chapman and Hall, London, UK, 1996.Google Scholar
- A. Jaimovich, O. Meshi, and N. Friedman. Template based inference in symmetric relational Markov random fields. In Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence, pages 191--199, Vancouver, Canada, 2007. AUAI Press.Google ScholarDigital Library
- S. Jiang, D. Lowd, and D. Dou. Learning to refine an automatically extracted knowledge base using Markov logic. In Proceedings of the IEEE International Conference on Data Mining (ICDM), Brussels, Belgium, 2012. IEEE Computer Society Press. Google ScholarDigital Library
- H. Kautz, B. Selman, and Y. Jiang. A general stochastic approach to solving problems with hard and soft constraints. In D. Gu, J. Du, and P. Pardalos, editors, The Satisfiability Problem: Theory and Applications, pages 573--586. American Mathematical Society, New York, NY, 1997.Google Scholar
- S. Kok and P. Domingos. Learning the structure of Markov logic networks. In Proceedings of the Twenty-Second International Conference on Machine Learning, pages 441--448, Bonn, Germany, 2005. ACM Press. Google ScholarDigital Library
- S. Kok and P. Domingos. Statistical predicate invention. In Proceedings of the Twenty-Fourth International Conference on Machine Learning, pages 433--440, Corvallis, OR, 2007. ACM Press. Google ScholarDigital Library
- S. Kok and P. Domingos. Extracting semantic networks from text via relational clustering. In Proceedings of the Nineteenth European Conference on Machine Learning, pages 624--639, Antwerp, Belgium, 2008. Springer.Google ScholarCross Ref
- S. Kok and P. Domingos. Hypergraph lifting for structure learning in Markov logic networks. In Proceedings of the Twenty-Sixth International Conference on Machine Learning, Montreal, Canada, 2009. ACM Press.Google ScholarDigital Library
- S. Kok, M. Sumner, M. Richardson, P. Singla, H. Poon, D. Lowd, and P. Domingos. The Alchemy system for statistical relational AI. Technical report, Department of Computer Science and Engineering, University of Washington, Seattle, WA, 2007. http://alchemy.cs.washington.edu.Google Scholar
- N. Lavrač and S. Džeroski. Inductive Logic Programming: Techniques and Applications. Ellis Horwood, Chichester, UK, 1994. Google ScholarDigital Library
- D. C. Liu and J. Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45(3):503--528, 1989.Google ScholarCross Ref
- J. W. Lloyd. Foundations of Logic Programming. Springer, Berlin, Germany, 1987. Google ScholarDigital Library
- D. Lowd and P. Domingos. Efficient weight learning for Markov logic networks. In Proceedings of the Eleventh European Conference on Principles and Practice of Knowledge Discovery in Databases, pages 200--211, Warsaw, Poland, 2007. Springer.Google ScholarCross Ref
- D. J. Lunn, A. Thomas, N. Best, and D. Spiegelhalter. WinBUGS -- a Bayesian modeling framework: concepts, structure, and extensibility. Statistics and Computing, 10:325--337, 2000. Google ScholarDigital Library
- L. Mihalkova and R. Mooney. Bottom-up learning of Markov logic network structure. In Proceedings of the Twenty-Fourth International Conference on Machine Learning, pages 625--632, Corvallis, OR, 2007. ACM Press. Google ScholarDigital Library
- M. Møller. A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks, 6:525--533, 1993. Google ScholarDigital Library
- A. Nath and P. Domingos. A language for relational decision theory. In Proceedings of the International Workshop on Statistical Relational Learning, Leuven, Belgium, 2009.Google Scholar
- M. Niepert. Markov chains on orbits of permutation groups. In Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence. UAIA Press, 2012.Google ScholarDigital Library
- M. Niepert, C. Meilicke, and H. Stuckenschmidt. A probabilistic-logical framework for ontology matching. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence. AAAI Press, 2010. Google ScholarDigital Library
- J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco, CA, 1988. Google ScholarDigital Library
- H. Poon and P. Domingos. Sound and efficient inference with probabilistic and deterministic dependencies. In Proceedings of the Twenty-First National Conference on Artificial Intelligence, pages 458--463, Boston, MA, 2006. AAAI Press. Google ScholarDigital Library
- H. Poon and P. Domingos. Joint inference in information extraction. In Proceedings of the Twenty-Second National Conference on Artificial Intelligence, pages 913--918, Vancouver, Canada, 2007. AAAI Press. Google ScholarDigital Library
- H. Poon and P. Domingos. Unsupervised semantic parsing. In Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing, Singapore, 2009. ACL. Google ScholarDigital Library
- H. Poon, P. Domingos, and M. Sumner. A general method for reducing the complexity of relational inference and its application to MCMC. In Proceedings of the Twenty-Third National Conference on Artificial Intelligence, pages 1075--1080, Chicago, IL, 2008. AAAI Press. Google ScholarDigital Library
- J. R. Quinlan. Learning logical definitions from relations. Machine Learning, 5:239--266, 1990. Google ScholarDigital Library
- M. Richardson and P. Domingos. Mining knowledge-sharing sites for viral marketing. In Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 61--70, Edmonton, Canada, 2002. ACM Press. Google ScholarDigital Library
- M. Richardson and P. Domingos. Markov logic networks. Machine Learning, 62:107--136, 2006. Google ScholarDigital Library
- S. Riedel. Improving the accuracy and efficiency of MAP inference for Markov logic. In Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence, pages 468--475, Helsinki, Finland, 2008. AUAI Press.Google ScholarDigital Library
- J. A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12:23--41, 1965. Google ScholarDigital Library
- D. Roth. On the hardness of approximate reasoning. Artificial Intelligence, 82:273--302, 1996. Google ScholarDigital Library
- P. Singla and P. Domingos. Discriminative training of Markov logic networks. In Proceedings of the Twentieth National Conference on Artificial Intelligence, pages 868--873, Pittsburgh, PA, 2005. AAAI Press. Google ScholarDigital Library
- P. Singla and P. Domingos. Memory-efficient inference in relational domains. In Proceedings of the Twenty-First National Conference on Artificial Intelligence, pages 488--493, Boston, MA, 2006. AAAI Press. Google ScholarDigital Library
- P. Singla and P. Domingos. Markov logic in infinite domains. In Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence, pages 368--375, Vancouver, Canada, 2007. AUAI Press.Google ScholarDigital Library
- P. Singla and P. Domingos. Lifted first-order belief propagation. In Proceedings of the Twenty-Third National Conference on Artificial Intelligence, pages 1094--1099, Chicago, IL, 2008. AAAI Press. Google ScholarDigital Library
- P. Singla, A. Nath, and P. Domingos. Approximate lifting techniques for belief propagation. In Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence. AAAI Press, 2014. Google ScholarDigital Library
- A. Srinivasan. The Aleph manual. Technical report, Computing Laboratory, Oxford University, 2000.Google Scholar
- B. Taskar, P. Abbeel, and D. Koller. Discriminative probabilistic models for relational data. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, pages 485--492, Edmonton, Canada, 2002. Morgan Kaufmann. Google ScholarDigital Library
- S. Wasserman and K. Faust. Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge, UK, 1994.Google ScholarCross Ref
- W. Wei, J. Erenrich, and B. Selman. Towards efficient sampling: Exploiting random walk strategies. In Proceedings of the Nineteenth National Conference on Artificial Intelligence, pages 670--676, San Jose, CA, 2004. AAAI Press. Google ScholarDigital Library
- M. Wellman, J. S. Breese, and R. P. Goldman. From knowledge bases to decision models. Knowledge Engineering Review, 7:35--53, 1992.Google ScholarCross Ref
- J. S. Yedidia, W. T. Freeman, and Y. Weiss. Generalized belief propagation. In T. Leen, T. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13, pages 689--695. MIT Press, Cambridge, MA, 2001. Google ScholarDigital Library
Index Terms
- Unifying Logical and Statistical AI
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