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Information Geometry Approach to Parameter Estimation in Hidden Markov Models. (arXiv:1705.06040v1 [math.ST])
来源于:arXiv
We consider the estimation of hidden Markovian process by using information
geometry with respect to transition matrices. We consider the case when we use
only the histogram of $k$-memory data. Firstly, we focus on a partial
observation model with Markovian process and we show that the asymptotic
estimation error of this model is given as the inverse of projective Fisher
information of transition matrices. Next, we apply this result to the
estimation of hidden Markovian process. For this purpose, we define an
exponential family of ${\cal Y}$-valued transition matrices. We carefully
discuss the equivalence problem for hidden Markovian process on the tangent
space. Then, we propose a novel method to estimate hidden Markovian process. 查看全文>>