Information Geometry Approach to Parameter Estimation in Hidden Markov Models

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.