Robust Estimation of Latent Tree Graphical Models: Inferring Hidden States With Inexact Parameters

Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here, we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete, reversible models, that significantly improves on previous sample requirement bounds. Our techniques are based on a new hidden state estimator that is robust to inaccuracies in estimated parameters. More precisely, we prove that latent tree models can be estimated with high probability in the so-called Kesten-Stigum regime with
O
(log
²
n
) samples, where
n
is the number of nodes.