Variable-order Markov model: Difference between revisions

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In [[stochastic processes]], a topic in [[mathematics]], '''Variable-order Markov (VOM) models''' are an important class of models that extend the well known [[Markov chain]] models. In contrast to the Markov chain models, where each [[random variable]] in a sequence with a [[Markov property]] depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on the specific observed realization.

This realization sequence is often called the ''context''; therefore the VOM models are also called ''context trees''.<ref name="Rissanen">{{cite journal|last = Rissanen|first = J.|title = A Universal Data Compression System|journal = IEEE Transactions on Information Theory|volume = 29|issue = 5|date = Sep 1983|pages = 656–664|url = http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?isnumber=22734&arnumber=1056741|doi = 10.1109/TIT.1983.1056741}}</ref> The flexibility in the number of conditioning random variables turns out to be of real advantage for many applications, such as [[statistical analysis]], [[Statistical classification|classification]] and [[prediction]].<ref name="Shmilovici">{{cite journal|last = Shmilovici|first = A.|author2=Ben-Gal, I. |title = Using a VOM Model for Reconstructing Potential Coding Regions in EST Sequences|journal = Computational Statistics|volume = 22|issue = 1|year = 2007|pages = 49–69|url=http://www.springerlink.com/content/a447865604519210/|doi = 10.1007/s00180-007-0021-8}}</ref><ref name="Begleiter">{{cite journal|last = Begleiter|first = R.|coauthors = El-Yaniv, R. and Yona, G.|title = On Prediction Using Variable Order Markov models|journal = Journal of Artificial Intelligence Research|volume = 22|year = 2004|pages = 385–421|url = http://www.jair.org/media/1491/live-1491-2335-jair.pdf}}</ref><ref name="Ben-Gal">{{cite journal|last = Ben-Gal|first = I.|coauthors = Morag, G. and Shmilovici, A.|title = CSPC: A Monitoring Procedure for State Dependent Processes|journal = Technometrics|volume = 45|issue = 4|year = 2003|pages = 293–311|url = http://www.eng.tau.ac.il/~bengal/Technometrics_final.pdf|doi = 10.1198/004017003000000122}}</ref>