Robust estimation of tree structured models
This work addresses the challenge of robust tree structure estimation in graphical models for applications like phylogenetics, but it appears incremental as it builds on and generalizes existing results.
The paper tackles the problem of learning undirected graphical models on trees from corrupted data, generalizing prior work on binary and Gaussian cases to linear latent tree models and characterizing conditions for consistent tree recovery using the Chow-Liu algorithm.
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.