Contents I. Introduction
Many modern digital platforms involve the acquisition of data over networks, while network data has a typically time-varying structure. For instance, measurements acquired on a sensor network or user data in a social network often vary over time. Such data can be modeled as time-varying graph signals, or time-vertex signals. In many practical applications, time-vertex signals may have missing observations due to issues such as sensor failure, connection loss, and partial availability of user statistics. Hence, the spatio-temporal interpolation of time-vertex signals arises as an important problem of interest. Similarly, in forecasting applications, one would like to predict future values of a time-vertex signal based on its past values. All these problems necessitate the computation of signal models that can accurately fit to the characteristics of data. Stationary graph process models are of potential interest for a wide range of data types where the correlation patterns between different nodes evolve in line with the topology of the graph, such as data resulting from message passing, diffusion, or filtering operations over irregular networks. In this work, we consider a setting where possibly partial observations of a collection of time-vertex signals are available, and study the problem of learning parametric stochastic graph processes from data for signal inference tasks such as interpolation and forecasting.
