February 2024 Identifiability in robust estimation of tree structured models
Marta Casanellas, Marina Garrote-López, Piotr Zwiernik
Author Affiliations +
Bernoulli 30(1): 1-21 (February 2024). DOI: 10.3150/22-BEJ1477

Abstract

Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar, Shah, and Caramanis showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Another paper by Katiyar, Hoffmann, and Caramanis follows a similar pattern for the Gaussian case. By framing this as a special phylogenetic recovery problem we largely generalize these two settings. Using the framework of linear latent tree models we discuss tree identifiability for binary data under a continuous corruption model (e.g. black/white images with greyscale corruption). For the Ising and the Gaussian tree model we also provide a characterisation of when the Chow-Liu algorithm consistently learns the underlying tree from the noisy data.

Funding Statement

MC and MGL were partially supported by Generalitat de Catalunya (AGAUR 2021SGR00603) and Spanish Government Agencia Estatal de Investigación, PID2019-103849GB-I00 AEI for both and CEX2020-001084-M AEI for MC. PZ was supported by the grant from the Natural Sciences and Engineering Research Council of Canada (NSERC, RGPIN-2023-03481).

Citation

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Marta Casanellas. Marina Garrote-López. Piotr Zwiernik. "Identifiability in robust estimation of tree structured models." Bernoulli 30 (1) 1 - 21, February 2024. https://doi.org/10.3150/22-BEJ1477

Information

Received: 1 February 2021; Published: February 2024
First available in Project Euclid: 8 November 2023

MathSciNet: MR4665022
zbMATH: 07764762
Digital Object Identifier: 10.3150/22-BEJ1477

Keywords: latent tree models , Learning tree structure , noisy data on trees

Vol.30 • No. 1 • February 2024
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