Bayesian Out-Trees

TL;DR

This paper introduces a Bayesian framework for modeling data with latent directed out-tree structures, enabling efficient inference and improved semi-supervised learning on various datasets.

Contribution

It develops a novel Bayesian out-tree model with closed-form likelihood computation, unifying iid and structured data modeling for improved learning algorithms.

Findings

Efficient closed-form likelihood computation using Tutte's matrix tree theorem.

Out-tree model performs well as a semi-parametric density estimator.

Applicable to taxonomy, phylogenetics, and standard iid datasets.

Abstract

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inference. The latent likelihood of the data and its gradients are computable in closed form via Tutte's directed matrix tree theorem using determinants and inverses of the out-Laplacian. This novel likelihood subsumes iid likelihood, is exchangeable and yields efficient unsupervised and semi-supervised learning algorithms. In addition to handling taxonomy and phylogenetic datasets the out-tree assumption performs surprisingly well as a semi-parametric density estimator on standard iid datasets. Experiments with unsupervised and semisupervised learning are shown on various UCI and taxonomy datasets.