Generic identification of binary-valued hidden Markov processes

Details Generic identification of binary-valued hidden Markov processes Generic identification of binary-valued hidden Markov processes

2011-01-19

arxiv.org/abs/1101.3712v5

Mathematics

Statistics Theory

28 pages

Scientific paper

The generic identification problem is to decide whether a stochastic process $(X_t)$ is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations which form a lower-dimensional subvariety in parameter space. So far partial answers to either the decision or the inference part have been given all of which depend on extra assumptions on the processes such as stationarity. Here we present a general solution for binary-valued hidden Markov processes. Our approach is rooted in algebraic statistics hence is geometric in nature. We find that the algebraic varieties associated with the probability distributions of binary-valued hidden Markov processes are zero sets of determinantal equations which draws a connection to well-studied objects from algebra. As a consequence, our solution allows for algorithmic implementation based on elementary (linear) algebraic routines.

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