Learning the structure of dynamic Bayesian networks from time series and steady state measurements
Dynamic Bayesian networks (DBN) are a class of graphical models that has become a standard tool for modeling various stochastic time-varying phenomena. In many applications, the primary goal is to infer the network structure from measurement data. Several efficient learning methods have been introduced for the inference of DBNs from time series measurements. Sometimes, however, it is either impossible or impractical to collect time series data, in which case, a common practice is to model the non-time series observations using static Bayesian networks (BN). Such an approach is obviously sub-optimal if the goal is to gain insight into the underlying dynamical model. Here, we introduce Bayesian methods for the inference of DBNs from steady state measurements. We also consider learning the structure of DBNs from a combination of time series and steady state measurements. We introduce two different methods: one that is based on an approximation and another one that provides exact computation. Simulation results demonstrate that dynamic network structures can be learned to an extent from steady state measurements alone and that inference from a combination of steady state and time series data has the potential to improve learning performance relative to the inference from time series data alone.
KeywordsDynamic Bayesian networks Steady state analysis Bayesian inference Markov chain Monte Carlo Trans-dimensional Markov chain Monte Carlo
- Çinlar, E. (1997). Introduction to stochastic processes (1st ed.). Englewood Cliffs: Prentice Hall. Google Scholar
- Friedman, N., Murphy, K., & Russell, S. (1998). Learning the structure of dynamic probabilistic networks. In Proceedings of fourteenth conference on uncertainty in artificial intelligence (UAI) (pp. 139–147). San Mateo: Morgan Kaufmann. Google Scholar
- Gelman, A., Roberts, G. O., & Gilks, W. R. (1996). Efficient Metropolis jumping rules. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian statistics (Vol. 5, pp. 599–607). Oxford: Oxford University Press. Google Scholar
- Giudici, P., Green, P. J., & Tarantola, C. (2000). Efficient model determination for discrete graphical models (Discussion paper No. 99-63). Available on-line at http://citeseer.ist.psu.edu/giudici00efficient.html.
- Hartemink, A., Gifford, D., Jaakkola, T., & Young, R. (2001). Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks. In Proceedings of pacific symposium on biocomputing (PSB 01) (Vol. 6, pp. 422–433). Singapore: World Scientific. Google Scholar
- Hartemink, A., Gifford, D., Jaakkola, T., & Young, R. (2002). Combining location and expression data for principled discovery of genetic regulatory network models. In Proceedings of pacific symposium on biocomputing (PSB 02) (Vol. 7, pp. 437–449). Singapore: World Scientific. Google Scholar
- Heckerman, D. (1998). A tutorial on learning with Bayesian networks. In M. I. Jordan (Ed.), Learning in graphical models (pp. 301–354). Cambridge: MIT Press. Google Scholar
- Lehoucq, R. B., Sorensen, D. C., & Yang, C. (1998). ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Philadelphia: SIAM. Google Scholar
- Markowetz, F. (2007). A bibliography on learning causal networks of gene interactions. Available on-line at http://www.molgen.mpg.de/~markowet/docs/network-bib.pdf.
- Murphy, K. P. (2002). Dynamic Bayesian networks: representation, inference and learning. PhD thesis, University of California, Berkeley. Google Scholar
- Nikovski, D. (1998). Learning stationary temporal probabilistic networks. In Conference on automated learning and discovery. Google Scholar
- Pe’er, D., Regev, A., Elidan, G., & Friedman, N. (2001). Inferring subnetworks from perturbed expression profiles. Bioinformatics, 17(Suppl. 1), 215S–224S. Google Scholar
- Pournara, I. (2004). Reconstructing gene regulatory networks by passive and active Bayesian learning. PhD thesis, Birkbeck College, University of London. Google Scholar
- Robert, C. P., & Casella, G. (2005). Monte Carlo statistical methods (2nd ed.), Berlin: Springer. Google Scholar
- Schäfer, J., & Strimmer, K. (2005). An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics, 21(5), 754–764. Google Scholar