Asymptotic Marginal Likelihood on Linear Dynamical Systems
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 time-series 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.
- Publication
- IEICE TRANSACTIONS on Information Vol.E97-D No.4 pp.884-892
- Publication Date
- 2014/04/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E97.D.884
- Type of Manuscript
- PAPER
- Category
- Artificial Intelligence, Data Mining
Authors
Takuto NAITO
Panasonic Corporation
Keisuke YAMAZAKI
Tokyo Institute of Technology
Keyword
Latest Issue
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Takuto NAITO, Keisuke YAMAZAKI, "Asymptotic Marginal Likelihood on Linear Dynamical Systems" in IEICE TRANSACTIONS on Information,
vol. E97-D, no. 4, pp. 884-892, April 2014, doi: 10.1587/transinf.E97.D.884.
Abstract: 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 time-series 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E97.D.884/_p
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@ARTICLE{e97-d_4_884,
author={Takuto NAITO, Keisuke YAMAZAKI, },
journal={IEICE TRANSACTIONS on Information},
title={Asymptotic Marginal Likelihood on Linear Dynamical Systems},
year={2014},
volume={E97-D},
number={4},
pages={884-892},
abstract={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 time-series 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.},
keywords={},
doi={10.1587/transinf.E97.D.884},
ISSN={1745-1361},
month={April},}
Copy
TY - JOUR
TI - Asymptotic Marginal Likelihood on Linear Dynamical Systems
T2 - IEICE TRANSACTIONS on Information
SP - 884
EP - 892
AU - Takuto NAITO
AU - Keisuke YAMAZAKI
PY - 2014
DO - 10.1587/transinf.E97.D.884
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E97-D
IS - 4
JA - IEICE TRANSACTIONS on Information
Y1 - April 2014
AB - 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 time-series 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.
ER -
English
