Continuous Time Bayesian Networks

By Uri Nodelman, Christian R. Shelton, Daphne Koller. Conference on Uncertainty in Artificial Intelligence, 2012

336 citations recorded by the source corpus.

In this paper we present a language for finite state continuous time Bayesian networks (CTBNs), which describe structured stochastic processes that evolve over continuous time. The state of the system is decomposed into a set of local variables whose values change over time. The dynamics of the system are described by specifying the behavior of each local variable as a function of its parents in a directed (possibly cyclic) graph. The model specifies, at any given point in time, the distribution over two aspects: when a local variable changes its value and the next value it takes. These distributions are determined by the variable's current value and the current values of its parents in the graph. More formally, each variable is modelled as a finite state continuous time Markov process whose transition intensities are functions of its parents. We present a probabilistic semantics for the language in terms of the generative model a CTBN defines over sequences of events. We list types of queries one might ask of a CTBN, discuss the conceptual and computational difficulties associated with exact inference, and provide an algorithm for approximate inference which takes advantage of the structure within the process.

Subfields: Artificial Intelligence, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/6fe0df37aae7246f485d4dc50a8cb7447487c567

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Citations in the corpus

Topics over time: a non-Markov continuous-time model of topical trends (2006, neutral): “In all cases, for simplicity, we ﬁx the number of topics T = 50 .”
Causal Learning for Partially Observed Stochastic Dynamical Systems (2018, background): “Nodelman et al. (2002, 2003) and Gunawardana et al. (2011) also considered learning problems in continuous-time models.”
GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series (2019, result): “In contrast with our work that focuses on continuous-time real-valued time series, continuous time modelling of time-to-events has been addressed with point processes (Mei & Eisner, 2017) and continuous time Bayesian networks (Nodelman et al., 2002).”
Graphical models for marked point processes based on local independence (2007, methodology): “Nodelman et al. (2002, 2003) comes closest to the kind of graphs that we will consider.”
Testing for Causality in Continuous Time Bayesian Network Models of High-Frequency Data (2016, methodology): “CTBNs were introduced by Nodelman et al. (2002) independently of Schweder (1970), who called them Composable processes.”
Automated adaptive inference of phenomenological dynamical models (2015, neutral): “Instead, each node’s distribution will in general depend on the entire history of all other variables [17].”
Structure learning in causal cyclic networks (2008, background): “In this case, alternative representations exist in the form of dynamic Bayesian networks (DBNs) (Friedman et al., 1999) and continuous-time Bayesian networks (CTBNs) (Nodelman et al., 2002, 2003).”