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Annals of Statistics
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on ℓ_1-regularized logistic regression, in which the neighborhood of any given node is estimated by performing logistic regression subject to an ℓ_1-constraint. The method is analyzed under high-dimensional scaling in which both the number of nodes p and maximum neighborhood size d are allowed to grow as a function of the number of observations n. Our main resultsdoi:10.1214/09-aos691 fatcat:uqtb3hfjhrdz7cpaujmnk43ole