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 which 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. 
Elchanan Mossel, Sebastien Roch, Allan Sly
math.PR cs.LG math.ST q-bio.PE stat.TH