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Conference Papers Year : 2020

Graphem: EM Algorithm for Blind Kalman Filtering Under Graphical Sparsity Constraints

Abstract

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 a multivariate 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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Dates and versions

hal-03066208 , version 1 (15-12-2020)

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Emilie Chouzenoux, Víctor Elvira. Graphem: EM Algorithm for Blind Kalman Filtering Under Graphical Sparsity Constraints. ICASSP 2020 - 45th International Conference on Acoustics, Speech and Signal Processing, May 2020, Barcelona, Spain. pp.5840-5844, ⟨10.1109/ICASSP40776.2020.9053646⟩. ⟨hal-03066208⟩
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