Learning Time-Varying Graphs From Online Data

This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the renders it model-independent, i.e., can be theoretically analyzed in its abstract formulation and then instantiated under a variety of model-dependent graph learning problems. is possible phrasing (time-varying) as composite optimization problem, where different functions regulate desiderata, e.g., data fidelity, sparsity or smoothness. Instrumental for findings recognizing that dependence majority (if not all) data-driven algorithms on exerted through empirical covariance matrix, representing sufficient statistic estimation problem. Its user-defined recursive update enables non-stationary environments, while iterative building novel tools explicitly take into account temporal dynamics, speeding up convergence implicitly including temporal-regularization solution. We specialize three well-known models, namely, Gaussian graphical model (GGM), structural equation (SEM), smoothness-based (SBM), we also introduce ad-hoc vectorization schemes structured matrices (symmetric, hollows, etc.) which are crucial perform correct gradient computations, other than enabling low-dimensional vector spaces hence easing storage requirements. After discussing theoretical guarantees proposed framework, corroborate with extensive numerical tests synthetic real