High-Dimensional Structure Estimation in Ising Models: Tractable Graph Families

We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. This algorithm requires only low-order statistics of the data and has a sample complexity of n =omega(J_{min}^{-2} log p), where p is the number of variables and $J_{\min}$ is the minimum (absolute) edge potential in the model. We also establish non-asymptotic necessary and sufficient conditions for structure estimation.