We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a tree-structured Ising model whose leaf node distribution is close in Total Variation Distance, improving on the results of prior work. On the testing side, we provide an efficient algorithm with fewer samples for testing whether two latent-tree Ising models have leaf-node distributions that are close or far in Total Variation distance. We obtain our algorithms by showing novel localization results for the total variation distance between the leaf-node distributions of tree-structured Ising models, in terms of their marginals on pairs of leaves.

翻译：我们提出了用于学习和检验潜树伊辛模型（即仅能观测其叶节点的伊辛模型）的时间与样本高效算法。在学习方面，我们获得了高效算法，能够学习总变差距离上叶节点分布接近的树结构伊辛模型，改进了先前工作的结果。在检验方面，我们提供了一种样本量更少的高效算法，用于检验两个潜树伊辛模型的叶节点分布是否在总变差距离上接近或远离。我们通过展示树结构伊辛模型叶节点分布之间总变差距离的新颖局部化结果（基于其叶对边际分布）获得了这些算法。