Robust estimation of latent tree graphical models: Inferring hidden states with inexact parameters

TL;DR

This paper introduces a new efficient estimation method for latent tree models that is robust to parameter inaccuracies, requiring only logarithmic squared samples in the number of nodes, applicable to Gaussian and discrete models.

Contribution

The authors develop a novel hidden state estimator that improves sample complexity bounds for latent tree models, including Gaussian and discrete types, in the Kesten-Stigum regime.

Findings

High-probability estimation with O(log^2 n) samples

Robustness to parameter inaccuracies in hidden state estimation

Applicable to both Gaussian and discrete latent tree models

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 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.