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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Veröffentlicht in:IEEE transactions on signal processing Jg. 70; S. 4757 - 4771
Hauptverfasser: Elvira, Victor, Chouzenoux, Emilie
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Schlagworte:
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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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3209016