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# Outlier-Robust Learning of Ising Models Under Dobrushin’s Condition

*Proceedings of Thirty Fourth Conference on Learning Theory*, PMLR 134:1645-1682, 2021.

#### Abstract

We study the problem of learning Ising models satisfying Dobrushin’s condition in the outlier-robust setting where a constant fraction of the samples are adversarially corrupted. Our main result is to provide the first computationally efficient robust learning algorithm for this problem with near-optimal error guarantees. Our algorithm can be seen as a special case of an algorithm for robustly learning a distribution from a general exponential family. To prove its correctness for Ising models, we establish new anti-concentration results for degree-2 polynomials of Ising models that may be of independent interest.