Graphical Inference in Linear-Gaussian State-Space Models

State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are possible when the model parameters are known, which is rarely the c...

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Vydané v:	IEEE transactions on signal processing Ročník 70; s. 4757 - 4771
Hlavní autori:	Elvira, Victor, Chouzenoux, Emilie
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.01.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Predmet:	Complex systems Convexity EM algorithm Engineering Sciences Estimation Graph theory graphical inference Inference Kalman filtering Kalman filters Mathematical models Numerical models Optimization Parameters primal-dual algorithms proximal methods Remote sensing Signal and Image processing Signal processing Signal processing algorithms Sparse matrices sparsity State space models State-space methods State-space modeling Statistical analysis Time series analysis graphical inference proximal methods primal-dual algorithms sparsity Kalman filtering EM algorithm State-space modeling
ISSN:	1053-587X, 1941-0476
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Abstract	State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are possible when the model parameters are known, which is rarely the case. The estimation of these parameters is crucial, not only for performing statistical analysis, but also for uncovering the underlying structure of complex phenomena. In this paper, we focus on the linear-Gaussian model, arguably the most celebrated SSM, and particularly in the challenging task of estimating the transition matrix that encodes the Markovian dependencies in the evolution of the multi-variate state. We introduce a novel perspective by relating this matrix to the adjacency matrix of a directed graph, also interpreted as the causal relationship among state dimensions in the Granger-causality sense. Under this perspective, we propose a new method called GraphEM based on the well sounded expectation-maximization (EM) methodology for inferring the transition matrix jointly with the smoothing/filtering of the observed data. We propose an advanced convex optimization solver relying on a consensus-based implementation of a proximal splitting strategy for solving the M-step. This approach enables an efficient and versatile processing of various sophisticated priors on the graph structure, such as parsimony constraints, while benefiting from convergence guarantees. We demonstrate the good performance and the interpretable results of GraphEM by means of two sets of numerical examples.
AbstractList	State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are possible when the model parameters are known, which is rarely the case. The estimation of these parameters is crucial, not only for performing statistical analysis, but also for uncovering the underlying structure of complex phenomena. In this paper, we focus on the linear-Gaussian model, arguably the most celebrated SSM, and particularly in the challenging task of estimating the transition matrix that encodes the Markovian dependencies in the evolution of the multi-variate state. We introduce a novel perspective by relating this matrix to the adjacency matrix of a directed graph, also interpreted as the causal relationship among state dimensions in the Granger-causality sense. Under this perspective, we propose a new method called GraphEM based on the well sounded expectation-maximization (EM) methodology for inferring the transition matrix jointly with the smoothing/filtering of the observed data. We propose an advanced convex optimization solver relying on a consensus-based implementation of a proximal splitting strategy for solving the M-step. This approach enables an efficient and versatile processing of various sophisticated priors on the graph structure, such as parsimony constraints, while benefiting from convergence guarantees. We demonstrate the good performance and the interpretable results of GraphEM by means of two sets of numerical examples.
Author	Chouzenoux, Emilie Elvira, Victor
Author_xml	– sequence: 1 givenname: Victor orcidid: 0000-0002-8967-4866 surname: Elvira fullname: Elvira, Victor email: victor.elvira@ed.ac.uk organization: School of Mathematics, University of Edinburgh, Edinburgh, U.K – sequence: 2 givenname: Emilie orcidid: 0000-0003-3631-6093 surname: Chouzenoux fullname: Chouzenoux, Emilie email: emilie.chouzenoux@centralesupelec.fr organization: Inria, CentraleSupélec, Centre de Vision Numérique, Université Paris-Saclay, Gif-sur-Yvette, France
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References	ref13 ref57 ref15 ref59 ref14 ref53 ref52 ref11 ref55 ref10 ref54 ref17 ref16 ref19 ref18 Thiesson (ref45) Doucet (ref8) 2009; 12 ref51 ref50 ref46 ref48 ref47 Briceo-Arias (ref56) 2021 ref42 ref41 Chiu (ref38) 2021 ref44 ref43 Pesquet (ref58) 2015; 16 ref49 ref7 ref9 ref4 ref3 ref6 ref5 ref40 ref35 ref34 ref37 ref36 ref31 ref75 ref30 ref74 Branchini (ref12) ref33 ref32 ref2 ref1 ref39 ref71 ref70 ref73 Bird (ref61) 2019 ref72 ref24 ref68 ref23 ref67 ref26 ref25 ref69 ref20 ref64 ref63 ref22 ref66 ref21 ref65 ref28 ref27 ref29 ref60 ref62
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SubjectTerms	Complex systems Convexity EM algorithm Engineering Sciences Estimation Graph theory graphical inference Inference Kalman filtering Kalman filters Mathematical models Numerical models Optimization Parameters primal-dual algorithms proximal methods Remote sensing Signal and Image processing Signal processing Signal processing algorithms Sparse matrices sparsity State space models State-space methods State-space modeling Statistical analysis Time series analysis
Title	Graphical Inference in Linear-Gaussian State-Space Models
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