Robust Gaussian Graphical Model Estimation with Arbitrary Corruption

We study the problem of estimating the highdimensional Gaussian graphical model where the data are arbitrarily corrupted. We propose a robust estimator for the sparse precision matrix in the highdimensional regime. At the core of our method is a robust covariance matrix estimator, which is based on truncated inner product. We establish the statistical guarantee of our estimator on both estimation error and model selection consistency. In particular, we show that provided that the number of corrupted samples n

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