Appears in collection : 2022 - T3 - WS1 - Non-linear and high dimensional inference

In settings where the covariance matrix is too large to even store, we would like to learn the partial correlation graph with as few covariance queries as possible (in a partial correlation graph, an edge exists if the corresponding entry in the inverse covariance matrix is non-zero). In recent work with Gabor Lugosi, Jakub Truszkowski, and Piotr Zwiernik, we showed that it is possible to use only a quasi-linear number of queries if the inverse covariance matrix is sparse enough, in the sense that the partial correlation graph resembles a tree on a global scale. I will explain these results and discuss extensions and applications.