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Asymptotic Marginal Likelihood on Linear Dynamical Systems
Takuto NAITO Keisuke YAMAZAKI
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E97D
No.4
pp.884892 Publication Date: 2014/04/01 Online ISSN: 17451361
DOI: 10.1587/transinf.E97.D.884 Type of Manuscript: PAPER Category: Artificial Intelligence, Data Mining Keyword: Bayesian learning, Kalman filter, timeseries data analysis,
Full Text: PDF(282.1KB)>>
Summary:
Linear dynamical systems are basic state space models literally dealing with underlying system dynamics on the basis of linear state space equations. When the model is employed for timeseries data analysis, the system identification, which detects the dimension of hidden state variables, is one of the most important tasks. Recently, it has been found that the model has singularities in the parameter space, which implies that analysis for adverse effects of the singularities is necessary for precise identification. However, the singularities in the models have not been thoroughly studied. There is a previous work, which dealt with the simplest case; the hidden state and the observation variables are both one dimensional. The present paper extends the setting to general dimensions and more rigorously reveals the structure of singularities. The results provide the asymptotic forms of the generalization error and the marginal likelihood, which are often used as criteria for the system identification.

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