Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T06:47:28.655Z Has data issue: false hasContentIssue false
  • English
  • Français

A BIRTH AND DEATH PROCESS FOR BAYESIAN NETWORK STRUCTURE INFERENCE

Published online by Cambridge University Press:  26 December 2017

Dale Jennings  and
Jem N. Corcoran
Dale Jennings
Affiliation:
Applied Mathematics, University of Colorado, 526 UCB, Boulder, Colorado, USA E-mail: corcoran@colorado.edu
Jem N. Corcoran
Affiliation:
Applied Mathematics, University of Colorado, 526 UCB, Boulder, Colorado, USA E-mail: corcoran@colorado.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Bayesian networks are convenient graphical expressions for high-dimensional probability distributions which represent complex relationships between a large number of random variables. They have been employed extensively in areas such as bioinformatics, artificial intelligence, diagnosis, and risk management. The recovery of the structure of a network from data is of prime importance for the purposes of modeling, analysis, and prediction. There has been a great deal of interest in recent years in the NP-hard problem of learning the structure of a Bayesian network from observed data. Typically, one assigns a score to various structures and the search becomes an optimization problem that can be approached with either deterministic or stochastic methods. In this paper, we introduce a new search strategy where one walks through the space of graphs by modeling the appearance and disappearance of edges as a birth and death process. We compare our novel approach with the popular Metropolis–Hastings search strategy and give empirical evidence that the birth and death process has superior mixing properties.

Keywords

Bayesian networksbirth and death processesstructure learning
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018 , pp. 615 - 625
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Akaike, H. (1981). Likelihood of a model and information criteria. Journal of Econometrics 16: 3–14.Google Scholar
2.Ambler, G.K. & Silverman, B.W. (2009). Perfect simulation of spatial point processes using dominated coupling from the past with application to a multiscale area-interaction point process. arXiv: 0903.2651.Google Scholar
3.Berthelsen, K.K. & Møller, J. (2002). A primer on perfect simulation for spatial point processes. Bulletin Brazilian Mathematical Society 33(3): 351–367.Google Scholar
4.Bockhorst, J., Craven, M., Page, D., Shavlik, J., & Glasner, J. (2003). A Bayesian network approach to operon prediction. Bioinformatics 19: 1227–1235.Google Scholar
5.Chen, T., He, H.L., & Church, G.M. (1999). Modeling gene expression with differential equations. In Pacific Symposium Biocomputing '99, pp. 29–40.Google Scholar
6.Cowell, R.G., Verall, R.J., & Yoon, Y.K. (2007). Modeling operational risk with Bayesian networks. Journal of Risk and Insurance 74: 795–827.Google Scholar
7.Curiac, D.I., Vasile, G., Banias, O., Volosencu, C., & Albu, A. (2009). Bayesian network model for diagnosis of psychiatric diseases. In Proceedings of the ITI 2009 31st International Conference on Information Technology Interfaces, pp. 61–66.Google Scholar
8.Dobra, A., Hans, C., Jones, B., Nevins, J.R., Yao, G., & West, M. (2004). Sparse graphical models for exploring gene expression data. Journal of Multivariate Analysis 90(1): 196–212.Google Scholar
9.Feller, W. (1968). An introduction to probability theory and its applications. vol I. London–New York–Sydney–Toronto: John Wiley & Sons.Google Scholar
10.Fenton, N. & Neil, M. (2013). Risk Assessment and Decision Analysis with Bayesian Networks. Boca Raton, FL: CRC Press, Taylor & Francis Group.Google Scholar
11.Friedman, N. & Koller, D. (2003). Being Bayesian about network structure. Machine Learning 50: 95–126.Google Scholar
12.Friedman, N., Linial, M., Nachman, I., & Pe‘er, D. (2000). Using Bayesian networks to analyze expression data. Journal of Computational Biology 7: 601–620.Google Scholar
13.Griffiths, T.L., Kemp, C., & Tenenbaum, J.B. (2008). Bayesian models of cognition. Cambridge Handbook of Computational Cognitive Modeling (Son, R., Ed.). Cambridge, MA: Cambridge University Press, pp. 59–100.Google Scholar
14.Heckerman, D. (1995). A tutorial on learning with Bayesian networks. Technical Report, Microsoft Corporation.Google Scholar
15.Herskovits, E. (1991). Computer-Based Probabilistic Network Construction. Ph.D. dissertation, Stanford University, Medical Information Science.Google Scholar
16.Husmeier, D. (2003). Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics 19(17): 2271–2282.Google Scholar
17.Imoto, S., Kim, S., Goto, T., Miyano, S., Aburatani, S., Tashiro, K., & Kuhara, S. (2003). Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network. Journal of Bioinformatics and Computational Biology 1: 231–252.Google Scholar
18.Jarvis, E.D., Smith, V.A., Wada, K., Rivas, M.V., McElroy, M., Smulders, T.V., Carninci, P., Hayashizaki, Y., Dietrich, F., Wu, X., McConnell, P., Yu, J., Wang, P.P., Hartemink, A.J., & Lin, S. (2002). A framework for integrating the Songbird brain. Journal of Comparative Physiology A 188: 961–980.Google Scholar
19.Korb, K. & Nicholson, A. (2003). Bayesian artificial intelligence. Boca Raton, FL: Chapman and Hall/CRC.Google Scholar
20.Madigan, D. & York, J. (1995). Bayesian graphical models for discrete data. International Statistical Review 63: 215–232.Google Scholar
21.Mourad, R., Sinoquet, C., & Leray, P. (2011). A hierarchical bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies. BMC Bioinformatics 12(1): 16.Google Scholar
22.Larrañaga, P., Calvo, B., Santana, R., Bielza, C., Galdiano, J., Inza, I., Lozano, J., Armañanzas, G.S.R., Pèrez, A., & Robles, V. (2005). Machine learning in bioinformatics. Briefings in Bioinformatics 7(1): 86–112.Google Scholar
23.Ong, I.M., Glasner, J.D., & Page, D. (2002). Modeling regulatory pathways in E. coli from time series expression profiles. Bioinformatics 18: 241–248.Google Scholar
24.Onisko, A., Druzdzel, M.J., & Wasyluk, H. (1999). A Bayesian network model for diagnosis of liver disorders. Proceedings of the Eleventh Conference on Biocybernetics and Biomedical Engineering 2: 842–846.Google Scholar
25.Preston, C. (1975). Spatial birth and death processes. Advances in Applied Probability 7(3): 465–466.Google Scholar
26.Ripley, B.D. (1977). Modelling spatial patterns. Journal of the Royal Statistical Society. Series B, 39(2): 172–212.Google Scholar
27.Tenenbaum, J.B., Griffiths, T.L., & Kemp, C. (2006). Theory-based Bayesian models of inductive learning and reasoning. Trends in Cognitive Sciences 10(7): 309–318.Google Scholar
28.Weber, P., Medina-Oliva, G., Simon, C., & Iung, B. (2012). Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas. Engineering Applications of Artificial Intelligence, 25(4): 671–682.Google Scholar
29.Xiang, Y., Pant, B., Eisen, A., Beddoes, M.P., & Pool, D. (1993). Multiply sectioned bayesian networks for neuromuscular diagnosis. Artificial Intelligence in Medicine 5: 293–314.Google Scholar