Information Geometrical Approach to Hidden Markov Process
| Project/Area Number |
16KT0017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Multi-year Fund |
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| Section | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2016-07-19 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥18,330,000 (Direct Cost: ¥14,100,000、Indirect Cost: ¥4,230,000)
Fiscal Year 2018: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Fiscal Year 2017: ¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
Fiscal Year 2016: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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| 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 / 時系列解析 / 脳磁図 / 連続変数 / 離散化 / 同値性問題 / Bregman divergence / emアルゴリズム / 統計数学 / 機械学習 / 人工知能 |
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| 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.
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| 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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Report
(5 results)
Research Products
(129 results)
