Distance-based Learning of Hypertrees

2025-11-26

AI Summary

This work investigates the theoretical learnability of hypergraphs via shortest-path queries (SP-queries). We focus on *ordered hypertrees*—a natural class with applications in biology and database theory—and present the first provably optimal online learning algorithm for them, which can be converted into an optimal offline algorithm. Our model is the first to strictly subsume, within the Fagin acyclic hypergraph hierarchy, a broad family of hypergraphs previously not efficiently learnable, achieving learnability with subquadratic query complexity. Furthermore, to capture distance degradation phenomena—e.g., in phylogenetic tree reconstruction—we introduce the *bounded-distance query* model and establish the first asymptotically tight query complexity bounds for learning general hypertrees. Collectively, our framework unifies online and offline learning paradigms, delivering both theoretical completeness and practical relevance.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Learning hypergraphs with shortest-path queries efficiently
• Provably optimal algorithm for orderly hypertrees in online setting
• Analyzing bounded distance queries for general hypertrees complexity

Innovation

• Online algorithm for orderly hypertrees
• Optimal offline algorithm transformation
• Bounded distance query complexity bounds