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We consider a new method for estimating the structure of Ising graphical models from data. We assume that the data is observed with error, so that it is, in a sense, unreliable. We propose and investigate an ``optimistic'' estimator; that is, an approach that seeks to correct the log-likelihood objective function when some amount of the data is known to be mismeasured. We derive an interior point algorithm that constructs our estimator efficiently, and demonstrate that it leads naturally to a parallel procedure for recovering the graphical structure of Ising models. We show that the optimistic estimator has performance comparable to, and exceeding, regularized logistic regression in the presence of noise.
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James A. Brofos and Rui Shu, "Optimistic and Parallel Ising Model Estimation." Dartmouth Computer Science Technical Report TR2015-766, January 2015.
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