  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.
