[Event website](https://pasc22.pasc-conference.org/program/schedule/index.html%3Fpost_type=page&p=11&sess=sess156.html) [Abstract & Slides](https://pasc22.pasc-conference.org/program/schedule/index.html%3Fpost_type=page&p=10&id=msa130&sess=sess156.html) In this talk we address the problem of learning large graphs represented by M-matrices via an $\ell_1$-regularized Gaussian maximum-likelihood approach. We build on top of a state-of-the-art sparse precision matrix estimation package and introduce two algorithms that learn M-matrices, that can be subsequently used for the estimation of graph Laplacian matrices. In the first one we propose an unconstrained method that follows a post processing approach in order to learn an M-matrix, and in the second one we implement a constrained approach based on sequential quadratic programming. We also demonstrate the effectiveness, accuracy, and performance of both algorithms. Our numerical examples and comparative results with modern open-source packages reveal that the proposed methods can accelerate the learning of graphs by up to 3 orders of magnitude, while accurately retrieving the latent graphical structure of the data. Furthermore, we conduct large scale case studies for the clustering of COVID-19 daily cases and the classification of image datasets to highlight the applicability in real-world scenarios.
