Graphical model selection refers to the problem of estimating the unknown graph structure given observations at the nodes in the model. We consider a challenging instance of this problem when some of the nodes are latent or hidden. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider the class of Ising models Markov on locally tree-like graphs, which are in the regime of correlation decay. We propose an efficient method for graph estimation, and establish its structural consistency when the number of samples n scales as n \Omega(\theta_{\min} {-\delta \eta(\eta 1)-2}\log p), where \theta_{\min} is the minimum edge potential, \delta is the depth (i.e., distance from a hidden node to the nearest observed nodes), and \eta is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.

Graphical model selection refers to the problem of estimating the unknown graph structure given observations at the nodes in the model. We consider a challenging instance of this problem when some of the nodes are latent or hidden. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider the class of Ising models Markov on locally tree-like graphs, which are in the regime of correlation decay. We propose an efficient method for graph estimation, and establish its structural consistency when the number of samples $n$ scales as $n \Omega(\theta_{\min} {-\delta \eta(\eta 1)-2}\log p)$, where $\theta_{\min}$ is the minimum edge potential, $\delta$ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and $\eta$ is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model.