High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence
University of California, Berkeley
Abstract
Given i.i.d. observations of a random vector X∈ℝp, we study the problem of estimating both its covariance matrix Σ*, and its inverse covariance or concentration matrix Θ*=(Σ*)−1. When X is multivariate Gaussian, the non-zero structure of Θ* is specified by the graph of an associated Gaussian Markov random field; and a popular estimator for such sparse Θ* is the ℓ1-regularized Gaussian MLE. This estimator is sensible even for for non-Gaussian X, since it corresponds to minimizing an ℓ1-penalized log-determinant Bregman divergence. We analyze its performance under high-dimensional scaling, in which the number of nodes in the graph p, the number of edges s, and the maximum node degree d, are allowed to grow as a…
Citation impact
- FWCI
- 54.71
- Percentile
- 100%
- References
- 43
Authors
4Topics & keywords
- Mathematics
- Covariance
- Estimation of covariance matrices
- Multivariate random variable
- Covariance matrix
- Combinatorics
- Covariance function
- Scatter matrix