Editing Dynamic Bayesian network

{{Short description|Probabilistic graphical model}}
[[File:Réseau bayésien dynamique.svg|frame|right|Dynamic Bayesian Network composed by 3 variables.]]
[[File:Réseau bayésien 3t.svg|frame|right|Bayesian Network developed on 3 time steps.]]
[[File:Réseau bayésien simplifié.svg|frame|right|Simplified Dynamic Bayesian Network. All the variables do not need to be duplicated in the graphical model, but they are dynamic, too.]]
A '''dynamic Bayesian network''' (DBN) is a [[Bayesian network]] (BN) which relates variables to each other over adjacent time steps. 

== History ==
A dynamic Bayesian network (DBN) 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.<ref>
{{cite journal
|url=http://research.microsoft.com/en-us/um/people/horvitz/dynamic_network_models_UAI_1992.pdf
|author1=Paul Dagum
|author-link=Paul Dagum
|author2=Adam Galper
|author2-link=Adam Galper
|author3=Eric Horvitz
|author3-link=Eric Horvitz
|title=Dynamic Network Models for Forecasting
|journal = Proceedings of the Eighth Conference on Uncertainty in Artificial Intelligence
|date=1992|publisher=AUAI Press|pages=41–48}}
</ref><ref>
{{cite journal
|url=http://research.microsoft.com/en-us/um/people/horvitz/FORECAST.HTM
|author1=Paul Dagum
|author-link=Paul Dagum
|author2=Adam Galper
|author2-link=Adam Galper
|author3=Eric Horvitz
|author3-link=Eric Horvitz
|author4=Adam Seiver
|author4-link=Adam Seiver
|title=Uncertain Reasoning and Forecasting
|journal = International Journal of Forecasting  |volume=11 |issue=1 |date=1995 |pages=73–87 |doi=10.1016/0169-2070(94)02009-e|doi-access=free
}}
</ref> Dagum developed DBNs to unify and extend traditional linear [[State Space Model|state-space models]] such as [[Kalman filter]]s, linear and normal forecasting models such as [[ARMA model|ARMA]] and simple dependency models such as [[hidden Markov model]]s into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains.<ref>
{{cite journal
|url=https://dslpitt.org/uai/papers/93/p64-dagum.pdf
|archive-url=https://web.archive.org/web/20150907230231/https://dslpitt.org/uai/papers/93/p64-dagum.pdf
|url-status=usurped
|archive-date=September 7, 2015
|author1=Paul Dagum
|author-link=Paul Dagum
|author2=Adam Galper
|author2-link=Adam Galper
|author3=Eric Horvitz
|author3-link=Eric Horvitz
|title=Temporal Probabilistic Reasoning: Dynamic Network Models for Forecasting
|journal = Knowledge Systems Laboratory. Section on Medical Informatics, Stanford University
|date=June 1991}}
</ref><ref>
{{cite journal
|url=http://www-ksl.stanford.edu/KSL_Abstracts/KSL-91-64.html
|author1=Paul Dagum
|author-link=Paul Dagum
|author2=Adam Galper
|author2-link=Adam Galper
|author3=Eric Horvitz
|author3-link=Eric Horvitz
|title=Forecasting Sleep Apnea with Dynamic Network Models
|journal = Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence 
|date=1993|publisher=AUAI Press|pages=64–71}}
</ref>

Today, DBNs are common in [[robotics]], and have shown potential for a wide range of [[data mining]] applications.  For example, they have been used in [[speech recognition]], [[digital forensics]], [[protein]] [[sequencing]], and [[bioinformatics]].  DBN is a generalization of [[hidden Markov models]] and [[Kalman filter]]s.<ref>{{cite book|author1=Stuart Russell|author-link=Stuart J. Russell|author2=Peter Norvig|author2-link=Peter Norvig|title=Artificial Intelligence: A Modern Approach|date=2010|publisher=[[Prentice Hall]]|isbn=978-0136042594|page=566|edition=Third|url=http://51lica.com/wp-content/uploads/2012/05/Artificial-Intelligence-A-Modern-Approach-3rd-Edition.pdf|accessdate=22 October 2014|quote='''dynamic Bayesian networks''' (which include hidden Markov models and Kalman filters as special cases)|url-status=dead|archiveurl=https://web.archive.org/web/20141020191456/http://51lica.com/wp-content/uploads/2012/05/Artificial-Intelligence-A-Modern-Approach-3rd-Edition.pdf|archivedate=20 October 2014}}</ref>

DBNs are conceptually related to probabilistic Boolean networks<ref>
{{cite journal
|pmc=1847796
|author1=Harri Lähdesmäki
|author-link=Harri Lähdesmäki
|author2=Sampsa Hautaniemi
|author2-link=Sampsa Hautaniemi
|author3=Ilya Shmulevich
|author3-link=Ilya Shmulevich
|author4=Olli Yli-Harja
|author4-link=Olli Yli-Harja
|title=Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks
|journal = Signal Processing
|volume=86
|issue=4
|date=2006|pages=814–834|pmid=17415411
|doi=10.1016/j.sigpro.2005.06.008
}}
</ref> and can, similarly, be used to model dynamical systems at steady-state.

== See also ==

* [[Recursive Bayesian estimation]]
* [[Probabilistic logic network]]
* [[Generalized filtering]]

== References ==
{{Reflist}}

== Further reading ==
*{{cite book|last=Murphy|first=Kevin|title=Dynamic Bayesian Networks: Representation, Inference and Learning|year=2002|publisher=UC Berkeley, Computer Science Division|url=http://www.cs.ubc.ca/~murphyk/Thesis/thesis.html}}
*{{cite book | citeseerx = 10.1.1.56.7874 | first = Zoubin | last = Ghahramani | chapter = Learning dynamic Bayesian networks | series = Lecture Notes in Computer Science | date = 1998 | title = Adaptive Processing of Sequences and Data Structures | volume = 1387 | pages = 168–197 | doi = 10.1007/BFb0053999 | isbn = 978-3-540-64341-8 }}
*{{cite conference | citeseerx = 10.1.1.75.2969 | last1 = Friedman | first1 = N. | last2 = Murphy | first2 = K. | last3 = Russell | first3 = S. | year = 1998 | title = Learning the structure of dynamic probabilistic networks | conference = UAI’98 | pages = 139–147 | publisher = Morgan Kaufmann }}
*{{cite journal | doi = 10.1109/ACCESS.2021.3105520 | last1 = Shiguihara | first1 = P. | last2 = De Andrade Lopes | first2 = A. | last3 = Mauricio | first3 = D. | year = 2021 | title = Dynamic Bayesian Network Modeling, Learning, and Inference: A Survey | publisher = IEEE Access | doi-access = free }}


== Software ==
* {{github|bayesnet/bnt}}: the Bayes Net Toolbox for Matlab, by Kevin Murphy, (released under a [[GNU General Public License|GPL license]])
* [https://web.archive.org/web/20150228005644/http://melodi.ee.washington.edu/gmtk/ 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.
* [http://www.bioss.ac.uk/~dirk/software/DBmcmc/ DBmcmc] : Inferring Dynamic Bayesian Networks with MCMC, for Matlab (free software)
* {{Google Code|globalmit|GlobalMIT Matlab toolbox}}: Modeling gene regulatory network via global optimization of dynamic bayesian network (released under a [[GNU General Public License|GPL license]])
* [http://staff.science.uva.nl/~jmooij1/libDAI/ 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]])
* [http://agrum.gitlab.io aGrUM]: C++ library (with Python bindings) for different types of PGMs including Bayesian Networks and Dynamic Bayesian Networks (released under the GPLv3)
* [https://github.com/sysbiolux/FALCON/ 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)

[[Category:Bayesian networks]]


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