Víctor Elvira: State-space models as graphs

Victor Elvira, University of Edinburgh
Date: Thursday 29 February 2024
Abstract: Modeling and inference in multivariate time series is central in statistics, signal processing, and machine learning. A fundamental question when analyzing multivariate sequences is the search for relationships between their entries (or the modeled hidden states), especially when the inherent structure is a directed (causal) graph. In such context, graphical modeling 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 complicated models.