thirdorderscientist

computational mechanics

Computational mechanics is a subdiscipline of the theory of stochastic processes motivated by finding the minimal representation of a stochastic process based on its predictive distribution. It is not this, and really warrants its own Wikipedia entry. For a good overview, see here, and here, while the course material still exists. An excellent review article is here.

The central object of study for computational mechanics is the causal or predictive states of the process, resulting from partitioning pasts of the process based on their predictive distributions, and the transitions between those states.

If the process you are interested is conditionally stationary, then you can learn its predictive states and the transitions between them from a (long enough) single realization of the process. One approach to this learning problem is Causal State Splitting Reconstruction.