Statistics Papers

Document Type

Journal Article

Date of this Version

7-2013

Publication Source

IEEE Transactions on Information Theory

Volume

59

Issue

7

Start Page

4357

Last Page

4373

DOI

10.1109/TIT.2013.2251927

Abstract

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.

Keywords

Gaussian processes, spectral analysis, state estimation, trees (mathematics), Gaussian models, Kesten-Stigum regime, computational biology, discrete models, hidden state estimator, image processing, latent tree graphical models, network tomography, reversible models, robust estimation, signal processing, biological system modeling, eigenvalues and eigenfunctions, estimation, graphical models, Markov processes, measurement, vegetation, Gaussian graphical models on trees, Kesten-Stigum (KS) reconstruction bound, Markov random fields on trees, phase transitions

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Date Posted: 27 November 2017

This document has been peer reviewed.