Sparse precision matrix estimation with missing observations

Sparse Gaussian graphical models have been extensively applied to detect the conditional independence structures from fully observed data. However, datasets with missing observations are quite common in many practical fields. In this paper, we propose a robust Gaussian graphical model with the covariance matrix being estimated from the partially observed data. We prove that the inverse of the Karush-Kuhn-Tucker mapping associated with the proposed model satisfies the calmness condition automatically. We also apply a linearly convergent alternating direction method of multipliers to find the solution to the proposed model. The numerical performance is evaluated on both the synthetic data and real data sets.