Identifiability in robust estimation of tree structured models

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.