A short introduction to observable operator models of discrete stochastic processes ∗
The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afford both mathematical simplicity and algorithmic efficiency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic representation of stationary, discrete stochastic processes. It is shown how any such process can be uniquely characterized by its abstract observable operators, yielding an abstract OOM of the process. All in all, observable operators open a lucid, general, and computationally extremely powerful avenue to discrete stochastic processes.