Distance-based Learning of Hypertrees

TL;DR

This paper introduces optimal algorithms for learning hypertrees using shortest-path queries, including models with bounded distance measurements, advancing understanding of hypergraph learning complexity.

Contribution

It presents the first provably optimal online and offline algorithms for a broad class of hypertrees called orderly hypertrees, and analyzes learning complexity with bounded distance queries.

Findings

Optimal online algorithm for orderly hypertrees

Transformation to optimal offline algorithm

Tight complexity bounds with bounded distance queries

Abstract

We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that we call orderly hypertrees. Our online algorithm can be transformed into a provably optimal offline algorithm. Orderly hypertrees can be positioned within the Fagin hierarchy of acyclic hypergraph (well-studied in database theory), and strictly encompass the broadest class in this hierarchy that is learnable with subquadratic SP-query complexity. Recognizing that in some contexts, such as evolutionary tree reconstruction, distance measurements can degrade with increased distance, we also consider a learning model that uses bounded distance queries. In this model, we demonstrate asymptotically tight complexity bounds for learning general hypertrees.