Compact Conformal Subgraphs

2026-02-07

AI Summary

This work addresses the limited practicality of traditional conformal prediction in structured tasks such as path planning and sequential recommendation, where it often yields overly large prediction sets. The authors propose the first framework that integrates conformal prediction with dense subgraph compression in hypergraphs, constructing minimal subgraphs that cover a specified probability mass while rigorously preserving statistical validity. Leveraging a weighted hypergraph model, the method introduces a parameterized minimum cut formulation and an efficient approximation algorithm, with monotonicity guarantees ensuring nestedness of prediction sets. Experiments on route planning and navigation simulations demonstrate that the approach consistently balances coverage and subgraph size within a constant factor, significantly outperforming baseline methods in prediction compactness without sacrificing validity.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce"graph-based conformal compression", a framework for constructing compact subgraphs that preserve statistical validity while reducing structural complexity. We formulate compression as selecting a smallest subgraph capturing a prescribed fraction of the probability mass, and reduce to a weighted version of densest $k$-subgraphs in hypergraphs, in the regime where the subgraph has a large fraction of edges. We design efficient approximation algorithms that achieve constant factor coverage and size trade-offs. Crucially, we prove that our relaxation satisfies a monotonicity property, derived from a connection to parametric minimum cuts, which guarantees the nestedness required for valid conformal guarantees. Our results on the one hand bridge efficient conformal prediction with combinatorial graph compression via monotonicity, to provide rigorous guarantees on both statistical validity, and compression or size. On the other hand, they also highlight an algorithmic regime, distinct from classical densest-$k$-subgraph hardness settings, where the problem can be approximated efficiently. We finally validate our algorithmic approach via simulations for trip planning and navigation, and compare to natural baselines.

Problem

• conformal prediction
• structured prediction
• graph compression
• prediction sets
• statistical validity

Innovation

• conformal prediction
• graph compression
• monotonicity
• densest k-subgraph
• hypergraph