Title: Information Geometry Approach to Parameter Estimation in Hidden Markov Models,
Abstract: 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. 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.