2016/05/31 by Alnur Ali, Ali, Alnur, Kshitij Khare +6
Decision Sciences · Engineering · Mathematics · #Algorithm #Applied mathematics #Computer science #Covariance #Covariance matrix #Diagonal #Estimation of covariance matrices #Estimator #Inverse #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Probabilistic and Robust Engineering Design #Range (aeronautics) #Sparse and Compressive Sensing Techniques #Statistics #Structural Health Monitoring Techniques #stat.ME
paper · pdf · doi:10.48550/arxiv.1606.00033
openalex publication_date 2016/05/31 · arxiv created 2016/10/14 · arxiv updated 2016/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce PseudoNet, a new pseudolikelihood-based estimator of the inverse covariance matrix, that has a number of useful statistical and computational properties. We show, through detailed experiments with synthetic and also real-world finance as well as wind power data, that PseudoNet outperforms related methods in terms of estimation error and support recovery, making it well-suited for use in a downstream application, where obtaining low estimation error can be important. We also show, under regularity conditions, that PseudoNet is consistent. Our proof assumes the existence of accurate estimates of the diagonal entries of the underlying inverse covariance matrix; we additionally provide a two-step method to obtain these estimates, even in a high-dimensional setting, going beyond the proofs for related methods. Unlike other pseudolikelihood-based methods, we also show that PseudoNet does not saturate, i.e., in high dimensions, there is no hard limit on the number of nonzero entries in the PseudoNet estimate. We present a fast algorithm as well as screening rules that make computing the PseudoNet estimate over a range of tuning parameters tractable.