2020/01/09 by Émilie Chouzenoux, Chouzenoux, Émilie, V́ıctor Elvira +1
Chemistry · Computer Science · #Bayesian Modeling and Causal Inference #Blind Source Separation Techniques #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.2001.03195
openalex publication_date 2020/01/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Modeling and inference with multivariate sequences is central in a number of\nsignal processing applications such as acoustics, social network analysis,\nbiomedical, and finance, to name a few. The linear-Gaussian state-space model\nis a common way to describe a time series through the evolution of a hidden\nstate, with the advantage of presenting a simple inference procedure due to the\ncelebrated Kalman filter. A fundamental question when analyzing multivariate\nsequences is the search for relationships between their entries (or the modeled\nhidden states), especially when the inherent structure is a non-fully connected\ngraph. In such context, graphical modeling combined with parsimony constraints\nallows to limit the proliferation of parameters and enables a compact data\nrepresentation which is easier to interpret by the experts. In this work, we\npropose a novel expectation-minimization algorithm for estimating the linear\nmatrix operator in the state equation of a linear-Gaussian state-space model.\nLasso regularization is included in the M-step, that we solved using a proximal\nsplitting Douglas-Rachford algorithm. Numerical experiments illustrate the\nbenefits of the proposed model and inference technique, named GraphEM, over\ncompetitors relying on Granger causality.\n