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2019 Fiscal Year Final Research Report

Information Geometrical Approach to Hidden Markov Process

Research Project

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Project/Area Number 16KT0017
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeMulti-year Fund
Section特設分野
Research Field Mathematical Sciences in Search of New Cooperation
Research InstitutionNagoya University

Principal Investigator

Hayashi Masahito  名古屋大学, 多元数理科学研究科, 教授 (40342836)

Project Period (FY) 2016-07-19 – 2020-03-31
Keywords隠れマルコフ過程 / 情報幾何 / 確率遷移行列 / 脳磁気図検査
Outline of Final Research Achievements

Hidden Markovian process is composed of visible and hidden variables, and only visible variables can be observed. This study focused on the k-order transition matrix on visible variables, and derived the method to estimate the transition matrix on visible and hidden variables from the k-order transition matrix on visible variables. In this method, we applied em-algorithm with respect to the geometrical structure over the space composed of k-order transition matrix on visible and hidden variables. Then, we clarified the asymptotic behavior of the error of the proposed method. Further, we studied the equivalence problem at the level of the tangent space. That is, we derived the necessary and sufficient condition for the equivalence in the tangent space.

Free Research Field

確率過程

Academic Significance and Societal Importance of the Research Achievements

隠れマルコフ過程は様々な現象に現れる数理モデルである.そのため,このモデルについて,解析し,研究することは極めて重要である.例えば,脳磁気図検査(MEG)の観測データは隠れマルコフ過程とみなすことができる.なぜなら,脳内の電気的活動である神経内の電流はマルコフ過程とみなすことはできるが,脳磁気図検査(MEG)によって直接計測できる磁場は,この電流を反映した確率過程であるため,隠れマルコフ過程に従うことになる.
本研究ではこのようなモデルに対する隠れマルコフ過程の応用についても研究した.

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Published: 2021-02-19  

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