Distance between a transition matrix and an instance

Question

I am trying to put a number to the distance of a sequence and how close it is to the original training corpus.

From the original training data, I got a markov transition matrix (TM).

So from the sequence I am trying to evaluate, I have all the transition probabilities.

I could calculate a new TM from the generated sequence (though much sparser), and for each element calculate the euclidian distance. I can calulate this in -log probs perhaps instead of probabilities, to be able to add them.

Would there be another approach to evalute how much the new sequences looks like the training data/model?

Answer 1

A distance between two statistical models can be calculated with Kullack-Leiber divergence (at least over the rows of the transition matrix). One could also use Euclidian distance between each element, see Herremans et al, 2014.