Dobrushin条件下Ising模型的离群鲁棒学习
Outlier-Robust Learning of Ising Models Under Dobrushin's Condition
摘要：
我们研究的问题，学习伊辛模型满足Dobrushin的条件下，在离群鲁棒设置的一个常数部分的样本是不利的损坏。我们的主要结果是提供第一个计算效率高的鲁棒学习算法，这个问题与近最佳的误差保证。我们的算法可以被看作是一个特殊的情况下，算法鲁棒学习的分布从一般的指数家庭。为了证明它的正确性的伊辛模型，我们建立了新的反浓度的结果的次数- $2$多项式的伊辛模型，可能是独立的利益。
英文摘要：
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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