Outlier-Robust Learning of Ising Models Under Dobrushin's Condition
Ilias Diakonikolas, Daniel M. Kane, Alistair M. Stewart, Yuxin Sun · arXiv (Cornell University) · 2021
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.