Learning and selection of dynamic Bayesian networks for online non-stationary process

Learning and selection of dynamic Bayesian networks for online non-stationary process

Matthieu Hourbracq Pierre-Henri Wuillemin Christophe Gonzales Philippe Baumard 

Sorbonne Université, CNRS, LIP6, UMR 7606, F-75005 Paris, France

Akheros S.A.S., France

Corresponding Author Email: 
firstName.lastName@lip6.fr; firstName.lastName@akheros.com
Page: 
75-109
|
DOI: 
https://doi.org/10.3166/RIA.32.75-109
Received: 
|
Accepted: 
|
Published: 
28 February 2018
| Citation
Abstract: 

Dynamic Bayesian Networks (DBNs) provide a principled scheme for modeling and learning conditional dependencies from complex multivariate time-series data. However, in most cases, the underlying generative Markov model is assumed to be homogeneous, meaning that neither its topology nor its parameters evolve over time. Therefore, learning a DBN to model a non-stationary process under this assumption will amount to poor predictions capabilities. Thus we build a framework to identify, in a streamed manner, transition times between underlying models and a framework to learn them in real time, without assumptions about their evolution. We propose a model for the dynamic of the transitions between modes stemming from Hidden semi-Markov Models (HsMMs) and Graphical Duration Models (GDMs). We show the method performances on simulated datasets.

Keywords: 

DBN, ns-DBN, tv-DBN, non-stationnary, learning, real time

1. Introduction
2. Réseaux bayésiens dynamiques (non stationnaires)
3. Apprentissage de processus non stationnaires
4. Graphical duration models
5. Expériences et résultats
6. Conclusions et travaux futurs
Remerciements

Ce travail est supporté par Akheros S.A.S./bourse ANRT CIFRE #2014/0268 et le projet européen SCISSOR H2020-ICT-2014-1 #644425.

  References

Akaike H. (1998). Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike, p. 199–213. Springer.

An X., Jutla D., Cercone N. (2006). Privacy intrusion detection using dynamic bayesian networks. In Acm international conference proceeding series, vol. 156, p. 208–215.

Barbu V., Boussemart M., Limnios N. (2004). Discrete-time semi-markov model for reliability and survival analysis. Communications in Statistics-Theory and Methods, vol. 33, no 11, p. 2833–2868.

Baum L. E., Petrie T. (1966). Statistical inference for probabilistic functions of finite state markov chains. The annals of mathematical statistics, vol. 37, no 6, p. 1554–1563.

Beran R. (1977). Minimum hellinger distance estimates for parametric models. The Annals of Statistics, p. 445–463.

Casella G., George E. I. (1992). Explaining the gibbs sampler. The American Statistician, vol. 46, no 3, p. 167–174.

Charitos T., Van Der Gaag L. C., Visscher S., Schurink K. A., Lucas P. J. (2009). A dynamic bayesian network for diagnosing ventilator-associated pneumonia in icu patients. Expert Systems with Applications, vol. 36, no 2, p. 1249–1258.

Chickering D., Geiger D., Heckerman D. (1995). Learning bayesian networks: Search methods and experimental results. In proceedings of fifth conference on artificial intelligence and statistics, p. 112–128.

Dean T., Kanazawa K. (1989). A model for reasoning about persistence and causation. Computational intelligence, vol. 5, no 2, p. 142–150.

Debar H., Dacier M., Wespi A. (1999). Towards a taxonomy of intrusion-detection systems. Computer Networks, vol. 31, no 8, p. 805–822.

Donat R., Bouillaut L., Aknin P., Leray P. (2008). Reliability analysis using graphical duration models. In Availability, reliability and security, 2008. ares 08. third international conference on, p. 795–800.

Donat R., Leray P., Bouillaut L., Aknin P. (2010). A dynamic bayesian network to represent discrete duration models. Neurocomputing, vol. 73, no 4, p. 570–577.

Duan J., Zeng J., Zhang D. (2009). A method for determination on hmm distance threshold. In Fuzzy systems and knowledge discovery, 2009. fskd’09. sixth international conference on, vol. 1, p. 387–391.

Getoor L., Friedman N., Koller D., Taskar B. (2001). Learning probabilistic models of relational structure. In Icml, vol. 1, p. 170–177.

Gonzales C., Dubuisson S., Manfredotti C. (2015). A new algorithm for learning non-stationary dynamic bayesian networks with application to event detection. In The twenty-eighth international

flairs conference.

Grzegorczyk M., Husmeier D. (2009). Non-stationary continuous dynamic bayesian networks. In Advances in neural information processing systems, p. 682–690.

Grzegorczyk M., Husmeier D. (2011). Non-homogeneous dynamic bayesian networks for continuous data. Machine Learning, vol. 83, no 3, p. 355–419.

Grzegorczyk M., Husmeier D., Edwards K. D., Ghazal P., Millar A. J. (2008). Modelling nonstationary gene regulatory processes with a non-homogeneous bayesian network and the allocation sampler. Bioinformatics, vol. 24, no 18, p. 2071–2078.

Heckerman D., Geiger D., Chickering D. M. (1995). Learning bayesian networks: The combination of knowledge and statistical data. Machine learning, vol. 20, no 3, p. 197–243.

Johansson M., Olofsson T. (2007). Bayesian model selection for markov, hidden markov, and multinomial models. IEEE signal processing letters, vol. 14, no 2, p. 129–132.

Kruegel C., Mutz D., RobertsonW., Valeur F. (2003). Bayesian event classification for intrusion detection. In Computer security applications conference, 2003. proceedings. 19th annual, p. 14–23.

Kullback S., Leibler R. A. (1951). On information and sufficiency. The annals of mathematical statistics, vol. 22, no 1, p. 79–86.

Lerner U., Parr R., Koller D., Biswas G. et al. (2000). Bayesian fault detection and diagnosis in dynamic systems. In Aaai/iaai, p. 531–537.

Liu T., Lemeire J. (2017). Efficient and effective learning of hmms based on identification of hidden states. Mathematical Problems in Engineering, vol. 2017.

Lloyd S. (1982). Least squares quantization in pcm. IEEE transactions on information theory,vol. 28, no 2, p. 129–137.

Mitra V., Nam H., Espy-Wilson C. Y., Saltzman E., Goldstein L. (2011). Gesture-based dynamic bayesian network for noise robust speech recognition. In Acoustics, speech and signal processing (icassp), 2011 ieee international conference on, p. 5172–5175.

Murphy K. P. (2002a). Dynamic bayesian networks: representation, inference and learning. Thèse de doctorat non publiée, University of California, Berkeley.

Murphy K. P. (2002b). Hidden semi-markov models (hsmms). unpublished notes, vol. 2.

Mutz D., Valeur F., Vigna G., Kruegel C. (2006). Anomalous system call detection. ACM Transactions on Information and System Security (TISSEC), vol. 9, no 1, p. 61–93.

Ourston D., Matzner S., Stump W., Hopkins B. (2003). Applications of hidden markov models to detecting multi-stage network attacks. In System sciences, 2003. proceedings of the 36th 

annual hawaii international conference on, p. 10–pp.

Pearl J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Francisco, CA, USA, Morgan Kaufmann Publishers Inc.

Perron P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica: Journal of the Econometric Society, p. 1361–1401.

Rabiner L. R. (1989). A tutorial on hidden markov models and selected applications in speech recognition. Proceedings of the IEEE, vol. 77, no 2, p. 257–286.

Rissanen J. (1978). Modeling by shortest data description. Automatica, vol. 14, no 5, p. 465–471.

Robinson J. W., Hartemink A. J. (2009). Non-stationary dynamic bayesian networks. In Advances in neural information processing systems, p. 1369–1376.

Robinson J. W., Hartemink A. J. (2010). Learning non-stationary dynamic bayesian networks. The Journal of Machine Learning Research, vol. 11, p. 3647–3680.

Schwarz G. (1978, 03). Estimating the dimension of a model. Ann. Statist., vol. 6, no 2, p. 461–464. Consulté sur http://dx.doi.org/10.1214/aos/1176344136

Sicard M., Baudrit C., Leclerc-Perlat M.,Wuillemin P.-H., Perrot N. (2011). Expert knowledge integration to model complex food processes. application on the camembert cheese ripening process. Expert Systems with Applications, vol. 38, no 9, p. 11804–11812.

Song L., Kolar M., Xing E. P. (2009). Time-varying dynamic bayesian networks. In Advances in neural information processing systems, p. 1732–1740.

Xu J., Shelton C. R. (2008). Continuous time bayesian networks for host level network intrusion detection. In Machine learning and knowledge discovery in databases, p. 613–627. Springer.

Xu J., Shelton C. R. (2010). Intrusion detection using continuous time bayesian networks. Journal of Artificial Intelligence Research, p. 745–774.

Yeung D.-Y., Ding Y. (2003). Host-based intrusion detection using dynamic and static behavioral models. Pattern recognition, vol. 36, no 1, p. 229–243.

Yu S.-Z. (2010). Hidden semi-markov models. Artificial intelligence, vol. 174, no 2, p. 215–243.

Zanero S., Serazzi G. (2008). Unsupervised learning algorithms for intrusion detection. In Network operations and management symposium, 2008. noms 2008. ieee, p. 1043–1048.

Zivot E., Andrews D. W. (2012). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics.