# High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition

arXiv: https://arxiv.org/abs/1802.06048 · HTML: https://mlsanity.com/paper/1802.06048/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2018.

## Built on by (most cited first, 1 of 1)

- [Lasso with Latents: Efficient Estimation, Covariate Rescaling, and Computational-Statistical Gaps](https://mlsanity.com/paper/2402.15409/) (2024)

## Abstract (arXiv)

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be small or controlled by a penalty function. Under moderate conditions on the population covariance/precision matrix itself and on the penalty function, we prove some consistency results for our estimators. A blockwise coordinate descent algorithm, which iteratively updates L and D, is then proposed to obtain the estimator in practice. Finally, various numerical experiments are presented: using simulated data, we show that our estimator performs quite well in terms of the Kullback-Leibler loss; using stock return data, we show that our method can be applied to obtain enhanced solutions to the Markowitz portfolio selection problem.