Seminar: State-space models as graphs

Abstract

Modelling and inference in multivariate time series is central in statistics, signal processing, and machine learning. A fundamental question when analysing multivariatesequences is the search for relationships between their entries (or the modelled hiddenstates), especially when the inherent structure is a directed (causal) graph. In such context,graphical modelling combined with sparsity constraints allows to limit the proliferation ofparameters and enables a compact data representation which is easier to interpret inapplications, 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 beinginterpreted as graphs. Then, we propose novel algorithms that exploit this new perspectivefor the estimation of the linear matrix operator and also the covariance matrix in the stateequation of a linear-Gaussian state-space model. Finally, we discuss the extension of thisperspective for the estimation of other model parameters in more challenging models.