Abstract
We present a novel approach to structure learning for graphical models. By using nonparametric estimates to model clique densities in decomposable models, both discrete and continuous distributions can be handled in a unified framework. Also, consistency of the underlying probabilistic model is guaranteed. Model selection is based on predictive assessment, with efficient algorithms that allow fast greedy forward and backward selection within the class of decomposable models. We show the validity of this structure learning approach on toy data, and on two large sets of gene expression data.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Lauritzen, S.L.: Graphical Models. Oxford Statistical Science Series, vol. 17. Clarendon Press, Oxford (1996)
Cowell, R.G., Dawid, A.P., Lauritzen, S.L., Spiegelhalter, D.J.: Probabilistic Networks and Expert Systems. In: Statistics for Engineering and Information Science, Springer, Heidelberg (1999)
Heckerman, D.: A tutorial on learning with Bayesian networks. In: Jordan, M.I. (ed.) Learning in Graphical Models, MIT Press, Cambridge (1998)
Song, Y., Goncalves, L., Perona, P.: Unsupervised learning of human motion. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(7), 814–827 (2003)
Banerjee, O., El Ghaoui, L., d’Aspremont, A., Natsoulis, G.: Convex optimization techniques for fitting sparse gaussian graphical models. In: De Raedt, L., Wrobel, S. (eds.) Proceedings of ICML06, pp. 89–96. ACM Press, New York (2006)
Hofmann, R., Tresp, V.: Nonlinear Markov networks for continuous variable. In: Jordan, M.I., Kearns, M.J., Solla, S.A. (eds.) Advances in Neural Information Processing Systems, vol. 10, MIT Press, Cambridge (1998)
Friedman, N., Nachman, I.: Gaussian process networks. In: Proceedings of UAI 2000, pp. 211–219. Morgan Kaufmann, San Francisco (2000)
Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using bayesian networks to analyze expression data. Journal of Computational Biology 7, 601–620 (2000)
Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402, C47 (1999)
Bouckaert, R.R.: Properties of Bayesian belief network learning algorithms. In: de Mantaras, R.L., Poole, D.L. (eds.) Proceedings of UAI 94, pp. 102–109. Morgan Kaufmann, San Francisco (1994)
de Campos, L.M.: Characterizations of decomposable dependency models. Journal of Artificial Intelligence Research 5, 289–300 (1996)
Giudici, P., Green, P.J.: Decomposable graphical Gaussian model determination. Biometrika 86, 785–801 (1999)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. In: Monographs on Statistics and Applied Probability, vol. 26, Chapman & Hall, Sydney, Australia (1986)
Deshpande, A., Garofalakis, M., Jordan, M.I.: Efficient stepwise selection in decomposable models. In: Breese, J., Koller, D. (eds.) Proceedings of UAI 2001, Morgan Kaufmann, San Francisco (2001)
Ibarra, L.: Fully dynamic algorithms for chordal graphs and split graphs. Technical Report DCS-262-IR. Department of Computer Science, University of Victoria, CA (2000)
Sleator, D.D., Tarjan, R.E.: Self-adjusting binary search trees. Journal of the ACM 32(3), 652–686 (1985)
Yeoh, E.J., et al.: Classification, subtype discovery, and prediction of outcome in pediatric acute lymphoblastic leukemia by gene expression profiling. Cancer Cell 1(2), 133–143 (2002)
Dejori, M., Schwaighofer, A., Tresp, V., Stetter, M.: Mining functional modules in genetic networks with decomposable graphical models. OMICS A Journal of Integrative Biology 8(2), 176–188 (2004)
Spira, A., Beane, J., Shah, V., Liu, G., Schembri, F., Yang, X., Palma, J., Brody, J.S.: Effects of cigarette smoke on the human airway epithelial cell transcriptome. Proceedings of the National Academy of Sciences of the United States of America 101(27), 10143–10148 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schwaighofer, A., Dejori, M., Tresp, V., Stetter, M. (2007). Structure Learning with Nonparametric Decomposable Models. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-74690-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74689-8
Online ISBN: 978-3-540-74690-4
eBook Packages: Computer ScienceComputer Science (R0)