The talk will provide an overview of graph signal processing (GSP)-based methods designed to learn an unknown network from nodal observations. Using signals to learn a graph is a central problem in network science and statistics, with results going back more than 50 years. The main goal of the talk is threefold: i) explaining in detail fundamental GSP-based methods and comparing those with classical methods in statistics, ii) putting forth a number of GSP-based formulations and algorithms able to address scenarios with a range of different operating conditions, and iii) briefly introducing generalizations to more challenging setups, including multi-layer graphs and learning in the presence of hidden nodal variables. Our graph learning algorithms will be designed as solutions to judiciously formulated constrained-optimization sparse-recovery problems. Critical to this approach is the codification of GSP concepts such as signal smoothness and graph stationarity into tractable constraints. Last but not least, while the focus will be on the so-called network association problem (a setup where observations from all nodes are available), the problem of network tomography (where some nodes remain unobserved, and which can be related to latent-variable graphical lasso) will also be discussed.
Antonio G. Marques received the telecommunications engineering degree and the Doctorate degree, both with highest honors, from the Carlos III University of Madrid, Spain, in 2002 and 2007, respectively. In 2007, he became a faculty of the Department of Signal Theory and Communications, King Juan Carlos University, Madrid, Spain, where he currently develops his research and teaching activities as a Full Professor and serves as Deputy to the President. From 2005 to 2015, he held different visiting positions at the University of Minnesota, Minneapolis. In 2016 and 2017 he was a visiting scholar at the University of Pennsylvania, Philadelphia. His current research focuses on signal processing for graphs, stochastic network optimization, and machine learning over graphs, with applications to communications, health, and transportation. Dr. Marques is a member of IEEE, EURASIP and the ELLIS society, having served these organizations in a number of posts. In recent years he has been an editor of three journals, a member of the IEEE Signal Processing Theory and Methods Technical Committee, a member of the IEEE Signal Processing Big Data Special Interest Group, the Technical Co-Chair of the IEEE CAMSAP Workshop, the General Co-chair of the IEEE Data Science Workshop, and the General Chair of the Graph Signal Processing Workshop. He currently is a Senior Area Editor for the IEEE Trans. Signal Processing and the Technical Chair for EUSIPCO 2023. Dr. Marques has also served as an external research proposal evaluator for different organizations, including the Spanish, French, Israeli, Dutch, Canadian, USA, and Swiss National Science Foundations. His work has received multiple journal and conference paper awards, with recent ones including a 2020 Young Best Paper Award of the IEEE SPS and the "2020 EURASIP Early Career Award", for his "significant contributions to network optimization and graph signal processing".