State-space Models as Graphs
Time: 10:00-11:00
Location: Turing Room (0.W100), Building 28, TU Delft
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Abstract: Modelling and inference in multivariate time series is central in statistics, signal processing, and machine learning. A fundamental question when analysing multivariate sequences is the search for relationships between their entries (or the modelled hidden states), especially when the inherent structure is a directed (causal) graph. In such context, graphical modelling combined with sparsity constraints allows to limit the proliferation of parameters and enables a compact data representation which is easier to interpret in applications, e.g., in inferring causal relationships of physical processes in a Granger sense. In this talk, we present a novel perspective consisting on state-space models being interpreted as graphs. Then, we propose novel algorithms that exploit this new perspective for the estimation of the linear matrix operator and also the covariance matrix in the state equation of a linear-Gaussian state-space model. Finally, we discuss the extension of this perspective for the estimation of other model parameters in more challenging models.
Bio: Víctor Elvira received the Ph.D. degree in wireless communications in 2011 from Universidad de Cantabria, Spain. He is a Professor in Statistics and Data Science in the School of Mathematics, University of Edinburgh, U.K. Previously, he held academic positions at Universidad Carlos III de Madrid, Spain, and IMT Lille Douai, France, and has been a visiting researcher at institutions including Stony Brook University, USA, and Paris-Dauphine University, France. His research interests include computational statistics, statistical signal processing, probabilistic machine learning, and Bayesian inference, with particular emphasis on importance sampling, sequential Monte Carlo methods, and state-space models. His work spans applications in climate tipping-point forecasting, statistical ecology, biomedical signal processing, wireless communications, energy forecasting, sensor networks, and target tracking. Prof. Elvira is a Fulbright Fellow, Marie Curie Fellow, Leverhulme Research Fellow, Alan Turing Fellow, and ELLIS Fellow. He received the 2024 EURASIP Early Career Award for contributions to importance sampling and particle filtering. He has served as an Associate Editor for the IEEE Transactions on Signal Processing and as an elected member of the IEEE Signal Processing Society Signal Processing Theory and Methods Technical Committee.