Learning and Testing Latent-Tree Ising Models Efficiently

Vardis Kandiros, Constantinos Daskalakis, Yuval Dagan, Davin Choo
Proceedings of Thirty Sixth Conference on Learning Theory, PMLR 195:1666-1729, 2023.

Abstract

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 \cite{cryan2001evolutionary}. 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v195-kandiros23a, title = {Learning and Testing Latent-Tree Ising Models Efficiently}, author = {Kandiros, Vardis and Daskalakis, Constantinos and Dagan, Yuval and Choo, Davin}, booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory}, pages = {1666--1729}, year = {2023}, editor = {Neu, Gergely and Rosasco, Lorenzo}, volume = {195}, series = {Proceedings of Machine Learning Research}, month = {12--15 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v195/kandiros23a/kandiros23a.pdf}, url = {https://proceedings.mlr.press/v195/kandiros23a.html}, abstract = {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 \cite{cryan2001evolutionary}. 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.} }
Endnote
%0 Conference Paper %T Learning and Testing Latent-Tree Ising Models Efficiently %A Vardis Kandiros %A Constantinos Daskalakis %A Yuval Dagan %A Davin Choo %B Proceedings of Thirty Sixth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2023 %E Gergely Neu %E Lorenzo Rosasco %F pmlr-v195-kandiros23a %I PMLR %P 1666--1729 %U https://proceedings.mlr.press/v195/kandiros23a.html %V 195 %X 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 \cite{cryan2001evolutionary}. 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.
APA
Kandiros, V., Daskalakis, C., Dagan, Y. & Choo, D.. (2023). Learning and Testing Latent-Tree Ising Models Efficiently. Proceedings of Thirty Sixth Conference on Learning Theory, in Proceedings of Machine Learning Research 195:1666-1729 Available from https://proceedings.mlr.press/v195/kandiros23a.html.

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