Learning latent tree models with small query complexity

TL;DR

This paper presents randomized algorithms for efficiently recovering latent tree structures in Gaussian graphical models with minimal query complexity, including analysis under noisy conditions and extensions to other distributions.

Contribution

It introduces optimal-order randomized procedures for latent tree recovery and provides statistical analysis for noisy distance data, extending to non-Gaussian cases.

Findings

Achieves optimal query complexity in structure recovery

Provides statistical analysis under noisy conditions

Extends methods to binary and non-paranormal distributions

Abstract

We consider the problem of structure recovery in a graphical model of a tree where some variables are latent. Specifically, we focus on the Gaussian case, which can be reformulated as a well-studied problem: recovering a semi-labeled tree from a distance metric. We introduce randomized procedures that achieve query complexity of optimal order. Additionally, we provide statistical analysis for scenarios where the tree distances are noisy. The Gaussian setting can be extended to other situations, including the binary case and non-paranormal distributions.