2022/12/04 by Samuel Rey, Rey, Samuel, Madeline Navarro +7
Computer Science · #Bayesian Modeling and Causal Inference #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning and ELM #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2212.01816
openalex publication_date 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is often the case that only a subset of nodes is observed while the rest remain hidden. Motivated by this, we propose a joint graph learning method that takes into account the presence of hidden (latent) variables. Intuitively, the presence of the hidden nodes renders the inference task ill-posed and challenging to solve, so we overcome this detrimental influence by harnessing the similarity of the estimated graphs. To that end, we assume that the observed signals are drawn from a Gaussian Markov random field with latent variables and we carefully model the graph similarity among hidden (latent) nodes. Then, we exploit the structure resulting from the previous considerations to propose a convex optimization problem that solves the joint graph learning task by providing a regularized maximum likelihood estimator. Finally, we compare the proposed algorithm with different baselines and evaluate its performance over synthetic and real-world graphs.