Compact Conformal Subgraphs

TL;DR

This work introduces graph-based conformal compression to convert large, graph-structured conformal prediction sets into compact subgraphs without sacrificing distribution-free validity. By recasting compression as a weighted hypergraph problem and applying a linear-programming rounding scheme, the authors obtain a bicriteria approximation that tightly trades off subgraph size and covered mass, with monotonic nested guarantees ensured via a parametric minimum-cut construction. The approach encompasses distribution-free variable-context, distribution-based, and fixed-context settings, and proves that the resulting conformal predictor is valid while achieving near-optimal compression in the high-coverage regime. Empirical results on navigation and trip-planning simulations demonstrate substantial compression relative to greedy baselines, while preserving the intended coverage $\ phi$. The framework thus enables reliable, scalable conformal uncertainty quantification for complex routing and scheduling tasks, with practical implications for real-time decision support and planning systems.

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.

Figures (3)

• Figure 1: Analysis of the synthetic urban routing scenario.
• Figure 2: Trip Planning simulation with planted core probability $\tau=0.8$. The x-axis is the conformal guarantee $\phi$, and the y-axis represents the ratio of selected vertices to the optimal core size.
• Figure 3: Real-world validation on Porto Taxi data (Airport $\to$ Center).

Theorems & Definitions (20)

• Definition 1: Monotonicity
• Lemma 1: Conformal Validity, proved in Appendix \ref{['app:conformal_proof']}
• Definition 2: Bicriteria approximation
• Example 1
• Theorem 1: Proved in Appendix \ref{['app:mainproof']}
• Theorem 2: Proved in Appendix \ref{['app:monotonicity']}
• Corollary 1: Proved in Appendix \ref{['app:monotonicity']}
• Theorem 3: Proved in Appendix \ref{['app:fixed']}
• Theorem 4
• proof