# Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption

arXiv: https://arxiv.org/abs/2309.08884 · HTML: https://mlsanity.com/paper/2309.08884/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 16 Sep 2023.

## Builds on (most cited first, 7 of 7)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Outlier Robust Mean Estimation with Subgaussian Rates via Stability](https://mlsanity.com/paper/2007.15618/) (2020)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Estimating Time-varying Brain Connectivity Networks from Functional MRI Time Series](https://mlsanity.com/paper/1310.3863/) (2013)
- [Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption](https://mlsanity.com/paper/2209.09624/) (2022)
- [G-AMA: Sparse Gaussian graphical model estimation via alternating minimization](https://mlsanity.com/paper/1405.3034/) (2014)

## Abstract (arXiv)

Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an online scenario even in the presence of arbitrary and adversarial data attacks. At each time step, data points, drawn nominally independently and identically from a multivariate Gaussian distribution, arrive. However, a certain fraction of these points may have been arbitrarily corrupted. We propose an online algorithm to estimate the sparse inverse covariance (i.e., precision) matrix despite this corruption. We provide the error-bound and convergence properties of the estimates to the true precision matrix under our algorithms.