Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption

TL;DR

This paper presents a robust online algorithm for estimating covariance and sparse precision matrices in Gaussian graphical models, effectively handling arbitrary data corruption and adversarial attacks in real-time.

Contribution

It introduces a modified trimmed-inner-product algorithm for online covariance estimation that is resilient to arbitrary data corruption, with proven error bounds and convergence guarantees.

Findings

The algorithm accurately estimates the true precision matrix despite data corruption.

Theoretical error bounds and convergence properties are established.

The method is effective in online scenarios with adversarial data attacks.

Abstract

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.