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...

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Bibliographic Details
Published in:IEEE transactions on information theory 2013-07, Vol.59 (7), p.4357-4373
Main Authors: Mossel, E., Roch, S., Sly, A.
Format: Article
Language:English
Subjects:
Applied sciences
Biological system modeling
Detection, estimation, filtering, equalization, prediction
Eigenvalues and eigenfunctions
Estimating techniques
Estimation
Exact sciences and technology
Gaussian graphical models on trees
Graphical models
Graphs
Image processing
Information theory
Information, signal and communications theory
Kesten-Stigum (KS) reconstruction bound
Markov processes
Markov random fields on trees
Measurement
Normal distribution
Parameter estimation
phase transitions
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Tomography
Vegetation
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2251927