Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption
This work addresses the vulnerability of Gaussian graphical models to adversarial data corruption, offering a robust solution for applications requiring real-time estimation in noisy environments.
The paper tackles the problem of robust online estimation of covariance and sparse precision matrices in Gaussian graphical models under arbitrary data corruption, proposing a modified trimmed-inner-product algorithm that provides error-bound and convergence guarantees to the true precision matrix.
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.