Abstract
In machine learning, graphical models like Bayesian networks are one of important visualization tools that can be learned from data to represent pictorially a complex system. In order to compare two complex systems (or one complex system functioning in two different contexts), one usually compares directly their representative graphs. However, with small sample size data, it is hard to learn the graph that represents precisely the system. That’s why ensemble methods (e.g. Bootstrapping, evolutionary algorithm, etc...) are proposed to learn from data of each system a set of graphs that represents more precisely this system. Then, for comparing two systems, one needs a mechanism to compare two sets of graphs. We propose in this work an approach based on multiple hypothesis testing and quasi essential graph (QEG) to compare two sets of Bayesian networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdi, H.: Bonferroni and Sidak corrections for multiple comparisons. Encyclopedia of measurement and statistics 1, 103–107 (2007)
Auliac, C., d’Alché Buc, F., Frouin, V.: Learning transcriptional regulatory networks with evolutionary algorithms enhanced with niching. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS (LNAI), vol. 4578, pp. 612–619. Springer, Heidelberg (2007)
Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society 57(1), 125–133 (1995)
Chickering, D.: Learning equivalence classes of Bayesian-network structures. Journal of Machine Learning Research 2, 445–498 (2002)
Delaplace, A., Brouard, T., Cardot, H.: Two evolutionary methods for learning bayesian network structures. In: International Conference on Computational Intelligence and Security, pp. 288–297 (2007)
Dudoit, S., Shaffer, J.P., Boldrick, J.C.: Multiple hypothesis testing in microarray experiments. Statist. Sci. 18(1), 71–103 (2003)
Friedman, N., Goldszmidt, M., Wyner, A.J.: Data analysis with bayesian net- works: A bootstrap approach. In: Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence, vol. 24, pp. 206–215. Morgan Kaufmann Publishers, San Francisco (1999)
Holm, S.: A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6(2), 65–70 (1979)
Larranaga, P., Poza, M., Yurramendi, Y., Murga, R.H., Kuijpers, C.M.H.: Structure learning of bayesian networks by genetic algorithms: A performance analysis of control parameters. IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 912–926 (1994)
Madigan, D., Andersson, S., Perlman, M., Volinsky, C.: Bayesian model averaging and model selection for markov equivalence classes of acyclic graphs. Communications in Statistics: Theory and Methods 25, 2493–2519 (1996)
Nguyen, H.T., Leray, P., Ramstein, G.: Summarizing and visualizing a set of bayesian networks with quasi essential graphs. ASMDA (Applied Stochastic Models and Data Analysis) International Society, Rome, Italy (to appear, 2011)
Opitz, D., Maclin, R.: Popular ensemble methods: An empirical study. Journal of Artificial Intelligence Research 11, 169–198 (1999)
Rodin, A.S., Boerwinkle, E.: Mining genetic epidemiology data with bayesian networks i: Bayesian networks and example application (plasma apoe levels). Bioinformatics 21(15), 3273–3278 (2005)
Wang, T., Yang, J.: A heuristic method for learning bayesian networks using discrete particle swarm optimization. Knowl. and Info. Sys. 24, 269–281 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, HT., Leray, P., Ramstein, G. (2011). Multiple Hypothesis Testing and Quasi Essential Graph for Comparing Two Sets of Bayesian Networks. In: König, A., Dengel, A., Hinkelmann, K., Kise, K., Howlett, R.J., Jain, L.C. (eds) Knowlege-Based and Intelligent Information and Engineering Systems. KES 2011. Lecture Notes in Computer Science(), vol 6882. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23863-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-23863-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23862-8
Online ISBN: 978-3-642-23863-5
eBook Packages: Computer ScienceComputer Science (R0)