  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.
