Skip to main content
eScholarship
Open Access Publications from the University of California

UC Santa Barbara

UC Santa Barbara Previously Published Works bannerUC Santa Barbara

Generalized pseudolikelihood methods for inverse covariance estimation

Abstract

Copyright 2017 by the author(s). 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 as well as real-world finance and 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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View