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'''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 variable]]s, in VOM models this number of conditioning [[random variable]]s may vary based on the specific observed realization.
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To construct the [[Markov chain]] of order 1 for the next character in
To construct the [[Markov chain]] of order 2 for the next character in
To construct the [[Markov chain]] of order three for the next character in
In practical settings there is seldom sufficient data to accurately estimate the [[exponential growth|exponential growing]] number of [[conditional probability]] components as the order of the [[Markov chain]] increases.
The Variable Order Markov model assumes that in realistic settings, there are certain realizations of states (represented by contexts) in which some past states are independent from the future states, accordingly, ''a great reduction in the number of model parameters can be achieved''[1].
==Definition==
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