# Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation

arXiv: https://arxiv.org/abs/1901.07693 · HTML: https://mlsanity.com/paper/1901.07693/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)

## Abstract (arXiv)

In a recent paper, Nguyen, Kuhn, and Esfahani (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this estimator. We develop a statistical theory which shows how to optimally choose the uncertainty size to minimize the associated Stein loss. Surprisingly, rather than the expected canonical square-root scaling rate, the optimal uncertainty size scales linearly with the sample size.