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

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3 Author(s)
Elchanan Mossel ; Department of Statistics and the Department of Computer Science, University of California, Berkeley, CA, USA ; S├ębastien Roch ; Allan Sly

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(log2n) samples, where n is the number of nodes.

Published in:

IEEE Transactions on Information Theory  (Volume:59 ,  Issue: 7 )