Generalized Pseudolikelihood Methods for Inverse Covariance Estimation
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Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:280288, 2017.
Abstract
We introduce PseudoNet, a new pseudolikelihoodbased 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 realworld finance as well as wind power data, that PseudoNet outperforms related methods in terms of estimation error and support recovery, making it wellsuited 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 twostep method to obtain these estimates, even in a highdimensional setting, going beyond the proofs for related methods. Unlike other pseudolikelihoodbased 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.
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