Hello.
I'm working on Markov Chains and I would like to know of efficient algorithms for constructing probabilistic transition matrices (of order n), given a text file as input.
I am not after one algorithm, but I'd rather like to build a list of such algorithms. Papers on such algorithms are also more than welcome, as any tips on terminology, etc. Notice that this topic bears a strong resemblance with n-gram identification algorithms.
Any help would be much appreciated.
It sounds like there are two possible questions, you should clarify which one:
The 'text file' contains probability values and "n" and you build the matrix directly, but how to code it? This question is trivial, so let's disregard it
The 'text file' contains something like signal data and you want to model it as a Markov Chain.
'Markov Chain' generally refers to a first order stochastic process, so I'm not sure then what you mean by "order", probably the size of the matrix, but that is not typical terminology. Anyway, for 1st-order, n x n matrix, discrete time random process, you should look at Viterbi Algorithm: http://en.wikipedia.org/wiki/Viterbi%5Falgorithm
Whenever dealing with Markov Models, I tend to end up looking at crm114 Discriminator. One, he goes into great detail about what different models there actually are (Markov isn't always the best, depending on what the application is) and provides general links and lots of background information on how probabilistic models work. While crm114 is generally used as some sort of SPAM identification tool, it is actually a more generic probability engine that I have used in other applications.