×

Structural learning about directed acyclic graphs from multiple databases. (English) Zbl 1256.68089

Summary: We propose an approach for structural learning of directed acyclic graphs from multiple databases. We first learn a local structure from each database separately, and then we combine these local structures together to construct a global graph over all variables. In our approach, we do not require conditional independence, which is a basic assumption in most methods.

MSC:

68Q32 Computational learning theory
68P15 Database theory
68R10 Graph theory (including graph drawing) in computer science
68T05 Learning and adaptive systems in artificial intelligence

Software:

TETRAD
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter, Probabilistic Networks and Expert Systems, Springer-Verlag, New York, NY, USA, 1999. · Zbl 0962.91532
[2] S. L. Lauritzen, Graphical Models, Oxford University Press, Oxford, UK, 1996. · Zbl 0871.14039 · doi:10.1353/ajm.1996.0015
[3] J. Pearl, Causality: Models, Reasoning, and Inference, Cambridge University Press, Cambridge, UK, 2000. · Zbl 1048.03502 · doi:10.1023/A:1018912507879
[4] P. Spirtes, C. Glymour, and R. Scheines, Causation, Prediction and Search, MIT Press, Cambridge, Mass, USA, 2nd edition, 2000. · Zbl 0806.62001
[5] X. Xie, Z. Geng, and Q. Zhao, “Decomposition of structural learning about directed acyclic graphs,” Artificial Intelligence, vol. 170, no. 4-5, pp. 422-439, 2006. · Zbl 1131.68510 · doi:10.1016/j.artint.2005.12.004
[6] T. Richardson and P. Spirtes, “Ancestral graph Markov models,” The Annals of Statistics, vol. 30, no. 4, pp. 962-1030, 2002. · Zbl 1033.60008 · doi:10.1214/aos/1031689015
[7] A. P. Dawid, “Conditional independence in statistical theory,” Journal of the Royal Statistical Society B, vol. 41, no. 1, pp. 1-31, 1979. · Zbl 0408.62004
[8] C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, “On the desirability of acyclic database schemes,” Journal of the Association for Computing Machinery, vol. 30, no. 3, pp. 479-513, 1983. · Zbl 0624.68087 · doi:10.1145/2402.322389
[9] C. Berge, Graphs and Hypergraphs, North-Holland Publishing, Amsterdam, The Netherlands, 2nd edition, 1976. · Zbl 0391.05028
[10] Z. Geng, K. Wan, and F. Tao, “Mixed graphical models with missing data and the partial imputation EM algorithm,” Scandinavian Journal of Statistics, vol. 27, no. 3, pp. 433-444, 2000. · Zbl 0972.62001 · doi:10.1111/1467-9469.00199
[11] I. Beinlich, H. Suermondt, R. Chavez, and G. Cooper, “The ALARM moni- toring system: a case study with two probabilistic inference techniques for belief networks,” in Proceedings of the 2nd European Conference on Artificial Intelligence in Medicine, pp. 247-256, Springer-Verlag, Berlin, Germany, 1989.
[12] D. Heckerman, “A tutorial on learning with Bayesian networks,” in Learning in Graphical Models, M. I. Jordan, Ed., pp. 301-354, Kluwer Academic, Dodrecht, The Netherlands, 1998. · Zbl 0921.62029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.