A Dynamic Bayesian Network (DBN) is a

Bayesian network A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...

(BN) which relates variables to each other over adjacent time steps. This is often called a ''Two-Timeslice'' BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by

Paul Dagum Paul may refer to: *Paul (given name), a given name (includes a list of people with that name) *Paul (surname), a list of people People Christianity *Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Chris ...

in the early 1990s at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as

Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimat ...

s, linear and normal forecasting models such as ARMA and simple dependency models such as

hidden Markov model A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an ob ...

s into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains. Today, DBNs are common in

robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...

, and have shown potential for a wide range of data mining applications. For example, they have been used in

speech recognition Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the m ...

digital forensics Digital forensics (sometimes known as digital forensic science) is a branch of forensic science encompassing the recovery, investigation, examination and analysis of material found in digital devices, often in relation to mobile devices and co ...

protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...

sequencing In genetics and biochemistry, sequencing means to determine the primary structure (sometimes incorrectly called the primary sequence) of an unbranched biopolymer. Sequencing results in a symbolic linear depiction known as a sequence which succ ...

, and

bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...

. DBN is a generalization of

hidden Markov models A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an ob ...

and

s. DBNs are conceptually related to Probabilistic Boolean Networks and can, similarly, be used to model dynamical systems at steady-state.

References

Software

* : the Bayes Net Toolbox for Matlab, by Kevin Murphy, (released under a

GPL license The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general u ...

)
Graphical Models Toolkit
(GMTK): an open-source, publicly available toolkit for rapidly prototyping statistical models using dynamic graphical models (DGMs) and dynamic Bayesian networks (DBNs). GMTK can be used for applications and research in speech and language processing, bioinformatics, activity recognition, and any time-series application.
DBmcmc
: Inferring Dynamic Bayesian Networks with MCMC, for Matlab (free software) * : Modeling gene regulatory network via global optimization of dynamic bayesian network (released under a

)
libDAI
C++ library that provides implementations of various (approximate) inference methods for discrete graphical models; supports arbitrary factor graphs with discrete variables, including discrete Markov Random Fields and Bayesian Networks (released under the

FreeBSD license BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD lice ...

)
aGrUM
C++ library (with Python bindings) for different types of PGMs including Bayesian Networks and Dynamic Bayesian Networks (released under the GPLv3)
FALCON
Matlab toolbox for contextualization of DBNs models of regulatory networks with biological quantitative data, including various regularization schemes to model prior biological knowledge (released under the GPLv3) Bayesian networks {{statistics-stub

See also

References

Further reading

Software