Robust estimation of tree structured Gaussian Graphical Model

Understand

Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model.

• If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model.
• Instead, suppose we only have noisy observations.
• If the noise at each node is independent, we can compute the sum of the covariance matrix and an unknown diagonal.