Robust Online Covariance and Sparse Precision Estimation Under Arbitrary
  Data Corruption
Tong Yao Shreyas Sundaram
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.