Outlier-Robust Learning of Ising Models Under Dobrushin's Condition

Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart, Yuxin Sun

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.

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