This chapter has described the theory behind the variable length Markov model and the learning algorithm. One problem of the VLMM is the choice of 
. It would be better to be able to estimate it and thus to have a parameter free algorithm.
Tino and Dorffner [45] try to solve this problem by using a completely different way of constructing the tree in the learning algorithm. They use a metric that represents how close two sequences are. This metric demands a parameter that can be interpreted as a learning parameter used in the same way as the learning parameter of a temporal difference learning [70]. A vector quantisation is then used to cluster subsequences into clusters that share the same suffix structure according to the metric. Unfortunately this approach does not eliminate the use of a parameter. However, it may be easier to find the right parameter for this learning algorithm. Experiments show that the result is sometimes better than the VLMM algorithm and sometimes equivalent.
Different measures of probability and different distances to compare probabilities have been described. We have seen some examples of generated text as well as generated trajectories in the appearance parameter space.
It has been shown that the use of the Matusita distance in the learning algorithm and the use of the maximum likelihood produced the best estimates of the probability distribution. However, for short training sets, we cannot trust totally the observed data, thus a combination of Kullback-Leibler divergence and Laplace's law of succession is better.