Latent tree models

TL;DR

Latent tree models are a versatile class of graphical models on trees, used across various fields, with a focus on their structure, learning algorithms, and fundamental limits.

Contribution

This paper provides a concise introduction to latent tree models, emphasizing the role of tree metrics in their structure, learning, and theoretical understanding.

Findings

Latent tree models encompass many well-known models like HMMs and Ising models.

Tree metrics are crucial for understanding the structure and learning algorithms.

The paper discusses fundamental limits of learning in latent tree models.

Abstract

Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. This article offers a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned.