Learning Sparse Graphs for Prediction and Filtering of Multivariate Data Processes

Complex data-generating processes are often described using graph models [1], [2]. In such models, each node represents a component with a signal. Directed links between nodes represent their influence on each other. For example, in the case of sensor networks, a distance-based graph is often used to characterize the underlying process [3]. In this paper, we are interested in graph models that are useful for prediction and filtering tasks. In the former case, the goal is to predict the signal values at a subset of nodes using information from the remaining nodes. In the latter case, the observed signal has been subject to some unknown perturbation and the goal is to identify the magnitude and source nodes of the perturbation [4]. To address both tasks, we aim to learn partial correlation graph models from a finite set of training data. Such graphs can be viewed as the minimal-assumption counterparts of conditional independence graphs [5], [6].