Robust estimation of tree structured models

TL;DR

This paper investigates the problem of learning tree-structured graphical models from corrupted data, extending previous work to more general settings including Gaussian and binary data, and analyzing the conditions for consistent tree recovery.

Contribution

It generalizes existing results by framing the problem as a phylogenetic recovery task and characterizes when the Chow-Liu algorithm can reliably learn the true tree from noisy data.

Findings

Tree identifiability under continuous corruption models.

Conditions for Chow-Liu algorithm consistency on noisy data.

Extension of recovery guarantees to Gaussian and binary models.

Abstract

Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar et al. showed that it is possible to recover trees from noisy binary data up to a small equivalence class of possible trees. Their other paper on the Gaussian case follows a similar pattern. 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. 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.