Large-Scale Graph Learning with Latent Variables
Graph learning, often called graphical model selection, is a well-studied problem. But motivated by challenges arising in estimating functional neuronal activity, we seek to learn the graph structure in the presence of latent variables and for extremely large-scale data with tens- to hundreds-of-thousands of nodes. To solve this, we propose a simple solution: hard thresholding existing graph selection estimators. We show that this approach is graph selection consistent in the presence of latent variables and at better statistical rates than previous approaches. Further, we leverage this result to yield a computationally fast and memory efficient method for learning large-scale graphs. We learn thresholded graphs on minipatches, or tiny subsets of both observations and nodes, and ensemble selection events to yield a provably consistent yet fast learner for large-scale graphs. We demonstrate our approaches via simulations on real examples to estimate functional connectivity from large-scale calcium imaging data. This is joint work with Minjie Wang and Tianyi Yao.
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