Abstract：To relax the homogeneity assumption of dynamic bayesian networks (DBNs), the non-homogeneous DBNs is proposed. In this paper, an improved reversible-jump Markov chain Monte Carlo (RJ-MCMC) algorithm is put forward by integrating the prior knowledge about the sliding window, namely APK-RJ-MCMC. The basic assumption of APK-RJ-MCMC is that the bigger the distribution distance between the backward window and the forward window of a time point is, the higher the probability of the time point as a changepoint becomes. Based on the above assumption, the rough probability of each time point as a changepoint is obtained. And it is considered as prior knowledge to guide birth, death and shift moves in RJ-MCMC algorithm during the changepoint sampling. Finally, the accept probability is thus adjusted. Experimental results on both the synthetic data and the real gene expression data show that the proposed APK-RJ-MCMC has a higher posterior probability and better AUC scores than the traditional algorithm does in changepoint detection.
[1] MURPHY K P. Dynamic Bayesian Networks: Representation, Infe-rence and Learning. Ph.D Dissertation. Berkeley, USA: University of California, 2002. [2] KOLLER D, FRIEDMAN N. Probabilistic Graphical Models: Principles and Techniques. Cambridge, USA: MIT Press, 2009. [3] XUAN X, MURPHY K. Modeling Changing Dependency Structure in Multivariate Time Series // Proc of the 24th International Confe-rence on Machine Learning. New York, USA: ACM, 2007: 1055-1062. [4] ARBEITMAN M N, FURLONG E E M, IMAM F, et al. Gene Expression during the Life Cycle of Drosophila Melanogaster. Science, 2002, 297(5590): 2270-2275. [5] TANTIPATHANANANDH C, BERGER-WOLF T, KEMPE D. A Framework for Community Identification in Dynamic Social Networks // Proc of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, USA: ACM, 2007: 717-726. [6] TALIH M, HENGARTNER N. Structural Learning with Time-Varying Components: Tracking the Cross-Section of Financial Time Series. Journal of the Royal Statistical Society (Statistical Methodology), 2005, 67(3): 321-341. [7] NIELSEN S H, NIELSEN T D. Adapting Bayes Network Structures to Non-stationary Domains. International Journal of Approximate Reasoning, 2008, 49(2): 379-397. [8] LEBRE S. Stochastic Process Analysis for Genomics and Dynamic Bayesian Networks Inference. Ph.D Dissertation. Eacutevry, France: Université d′Evry-Val d′Essonne, 2007. [9] GRZEGORCZYK M, HUSMEIER D. Non-stationary Continuous Dynamic Bayesian Networks // BENGIO Y, SCHUURMANS D, LAFFERTY J D, et al., eds. Advances in Neural Information Processing Systems 22. Cambridge, USA: MIT Press, 2009: 682-690. [10] HUSMEIER D, DONDELINGER F, LEBRE S. Inter-Time Se-gment Information Sharing for Non-homogeneous Dynamic Bayesian Networks // LAFFERTY J D, WILLIAMS C K I, SHAWE-TAYLOR J, et al., eds. Advances in Neural Information Processing Systems 23. Cambridge, USA: MIT Press, 2010: 901-909. [11] ROBINSON J W, HARTEMINK A J. Learning Non-stationary Dynamic Bayesian Networks. Journal of Machine Learning Research, 2010, 11: 3647-3680. [12] DONDELINGER F, LEBRE S, HUSMEIER D. Heterogeneous Continuous Dynamic Bayesian Networks with Flexible Structure and Inter-Time Segment Information Sharing // Proc of the 27th International Conference on Machine Learning. Anderson, USA: Omnipress, 2010: 303-310. [13] GRZEGORCZYK M, HUSMEIER D. Bayesian Regularization of Non-homogeneous Dynamic Bayesian Networks by Globally Coupling Interaction Parameters // Proc of the 15th International Conference on Artificial Intelligence and Statistics. Cambridge, USA: MIT Press, 2012: 467-476. [14] GRZEGORCZYK M, HUSMEIER D. Regularization of Non-homogeneous Dynamic Bayesian Networks with Global Information-Coupling Based on Hierarchical Bayesian Models. Machine Learning, 2013, 91(1): 105-154. [15] DONDELINGER F, LBRE S, HUSMEIER D. Non-homogeneous Dynamic Bayesian Networks with Bayesian Regularization for Infe-rring Gene Regulatory Networks with Gradually Time-Varying Structure. Machine Learning, 2013, 90(2): 191-230. [16] GRZEGORCZYK M. A Non-homogeneous Dynamic Bayesian Network with a Hidden Markov Model Dependency Structure among the Temporal Data Points. Machine Learning, 2016, 102(2): 155-207. [17] GRZEGORCZYK M, HUSMEIER D, EDWARDS K D, et al. Modelling Non-stationary Gene Regulatory Processes with a Non-homogeneous Bayesian Network and the Allocation Sampler. Bioinformatics, 2008, 24(18): 2071-2078. [18] KOLAR M, SONG L, XING E P. Sparsistent Learning of Varying-Coefficient Models with Structural Changes // BENGIO Y, SCHUURMANS D, LAFFERTY J D, et al., eds. Advances in Neural Information Processing Systems 22. Cambridge, USA: MIT Press, 2009: 1006-1014. [19] SONG L, KOLAR M, XING E P. Time-Varying Dynamic Bayesian Networks // BENGIO Y, SCHUURMANS D, LAFFERTY J D, et al., eds. Advances in Neural Information Processing Systems 22. Cambridge, USA: MIT Press, 2009: 1732-1740. [20] AHMED A, XING E P. Recovering Time-Varying Networks of Dependencies in Social and Biological Studies. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(29): 11878-11883. [21] ROBINSON J W, HARTEMINK A J. Non-stationary Dynamic Bayesian Networks // BENGIO Y, SCHUURMANS D, LAFFERTY J D, et al., eds. Advances in Neural Information Processing Systems 22. Cambridge, USA: MIT Press, 2009: 1369-1376. [22] WANG K J, ZHANG J Y, SHEN F S, et al. Adaptive Learning of Dynamic Bayesian Networks with Changing Structures by Detecting Geometric Structures of Time Series. Knowledge and Information Systems, 2008, 17(1): 121-133. [23] GONZALES C, DUBUISSON S, MANFREDOTTI C. A New Algorithm for Learning Non-stationary Dynamic Bayesian Networks with Application to Event Detection // Proc of the 28th International Florida Artificial Intelligence Research Society Conference on Inte-lligence. New York, USA: AAAI, 2015: 564-569. [24] PUNSKAYA E, ANDRIEU C, DOUCET A, et al. Bayesian Curve Fitting Using MCMC with Applications to Signal Segmentation. IEEE Trans on Signal Processing, 2002, 50(3): 747-758. [25] GREEN P J. Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika, 1995, 82(4): 711-732.
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