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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 in the early 1990s at Stanford University'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 estima ...
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 interdisciplinarity, 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 human ...
, 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 ma ...
,
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 comp ...
,
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, respon ...
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 succi ...
, 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 combin ...
. 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
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 estima ...
s. DBNs are conceptually related to Probabilistic Boolean Networks and can, similarly, be used to model dynamical systems at steady-state.


See also

*
Recursive Bayesian estimation In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using in ...
*
Probabilistic logic network A probabilistic logic network (PLN) is a conceptual, mathematical, and computational approach to uncertain inference; inspired by logic programming, but using probabilities in place of crisp (true/false) truth values, and fractional uncertainty i ...
*
Generalized filtering Generalized filtering is a generic Bayesian filtering scheme for nonlinear state-space models. It is based on a variational principle of least action, formulated in generalized coordinates of motion. Note that "generalized coordinates of motion" a ...


References


Further reading

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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 ...
)
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
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 ...
)
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