Real Time Learning of Non-stationary Processes with Dynamic Bayesian Networks
Dynamic Bayesian Networks (DBNs) provide a principled scheme for modeling and learning conditional dependencies from complex multivariate time-series data and have been used in a wide scope. However, in most cases, the underlying generative Markov model i
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Sorbonne Universit´es, UPMC Univ Paris 6, CNRS, UMR 7606 LIP6, Paris, France {matthieu.hourbracq,pierre-henri.wuillemin,christophe.gonzales}@lip6.fr 2 Akheros, Paris, France {matthieu.hourbracq,philippe.baumard}@akheros.com
Abstract. Dynamic Bayesian Networks (DBNs) provide a principled scheme for modeling and learning conditional dependencies from complex multivariate time-series data and have been used in a wide scope. 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. To account for non-stationary processes, we build on 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 show the method performances on simulated datasets. The goal of the system is to model and predict incongruities for an Intrusion Dectection System (IDS) in near real-time, so great care is attached to the ability to correctly identify transitions times. Our preliminary results reveal the precision of our algorithm in the choice of transitions and consequently the quality of the discovered networks. We finally suggest future works. Keywords: DBN · ns-DBN Real time · Change point
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Introduction
In many fields, particularly in information systems and biology modeling, observed processes evolve over time on many scales. Their system states change with time, describing complex trajectories. Some events or entities may influence others at any given time, but those correlations do not necessarily hold forever. Which entity influences another may therefore vary, and any model wishing to capture such a process, without observing the mechanism responsible for such changes, cannot be stationary, that is its structure and/or parameters need to evolve with time too. Otherwise, only one behavior is seen, averaging all observations. Since we wish to model the behavior of information systems within a network of computers - in real time - it seems reasonable to assume c Springer International Publishing Switzerland 2016 J.P. Carvalho et al. (Eds.): IPMU 2016, Part I, CCIS 610, pp. 338–350, 2016. DOI: 10.1007/978-3-319-40596-4 29
Real Time Learning of Non-stationary Processes with DBNs
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non-stationarity of the observed processes. Indeed, any program or application can accept a wide range of inputs, communicate with other programs, and paths chosen by the process (where it goes and what it does) are often at least input dependent. Thereby, we need a framework for learning non-stationary processes, in real time, and set our focus on non-stationary dynamic Bayesian networks. Dynamic Bayesian Networks [5,13] are a probabilistic graphical formalism describing, through conditional dependencies, complex dynamical systems under uncertainty. Yet, the use
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