Equations for hidden Markov models
نویسنده
چکیده
In the following, we will outline how to obtain invariants for hidden Markov and related models, based on an approach which, in its most prevalent application, served to solve the identifiability problem for hidden Markov processes (HMPs) in 1992 [13]. Some of its foundations had been layed in the late 50’s and early 60’s in order to get a grasp of problems related to that of identifying HMPs [5, 11, 6, 7, 8, 12]. The approach can be viewed as being centered around the definition of finite-dimensional discrete-time, discretevalued stochastic processes (referred to as discrete random processes in the following). It Examples of finite-dimensional discrete random processes other than HMPs are quantum random walks (QRWs). QRWs have been brought up mostly to emulate Markov chain related algorithms (e.g. Markov Chain Monte Carlo techniques) on quantum computers [1]. In the following, we will introduce finite-dimensional string functions and formally describe how to view discrete random processes as string functions.
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