Compact Conformal Subgraphs

Conformal prediction provides rigorous uncertainty guarantees for model outputs but can produce prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce \emph{graph-based conformal compression}, a framework for constructing compact subgraphs that preserve the statistical validity of conformal prediction while reducing structural complexity. We study a formulation that selects a smallest subgraph capturing a prescribed fraction of conditional 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. Our results highlight an algorithmic regime, distinct from classical densest-$k$-subgraph hardness settings, where the problem can be approximated efficiently, bridging conformal prediction with combinatorial graph compression. We finally validate our algorithmic approach on synthetic and real-world instances of trip planning and navigation, showing in each case that our approach handily beats natural baselines.