期刊
2020 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING
卷 -, 期 -, 页码 5840-5844出版社
IEEE
DOI: 10.1109/icassp40776.2020.9053646
关键词
Kalman filtering; state-space model; graphical inference; sparsity; proximal methods; EM algorithm
资金
- Agence Nationale de la Recherche of France under PISCES project [ANR-17-CE40-0031-01]
- Agence Nationale de la Recherche of France under MAJIC project [ANR-17-CE40-0004-01]
- Agence Nationale de la Recherche (ANR) [ANR-17-CE40-0004] Funding Source: Agence Nationale de la Recherche (ANR)
Modeling and inference with multivariate sequences is central in a number of signal processing applications such as acoustics, social network analysis, biomedical, and finance, to name a few. The linear-Gaussian state-space model is a common way to describe a time series through the evolution of a hidden state, with the advantage of presenting a simple inference procedure due to the celebrated Kalman filter. A fundamental question when analyzing amultivariate sequence is the search for relationships between its entries (or the entries of the modeled hidden state), especially when the inherent structure is a non-fully connected graph. In such context, graphical modeling combined with parsimony constraints allows to limit the proliferation of parameters and enables a compact data representation which is easier to interpret by the experts. In this work, we propose a novel expectation-maximization algorithm for estimating the linear matrix operator in the state equation of a linear-Gaussian state-space model. Lasso regularization is included in the M-step, that we solve using a proximal splitting Douglas-Rachford algorithm. Numerical experiments illustrate the benefits of the proposed model and inference technique, named GraphEM, over competitors relying on Granger causality.
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