Compact Conformal Subgraphs

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 calibration. Our results therefore not only highlight an algorithmic regime, distinct from classical densest-k-subgraph hardness settings, where the problem can be approximated efficiently, but also bridge conformal prediction with combinatorial graph compression via monotonicity. We finally validate our algorithmic approach via simulations for trip planning and navigation, and compare to natural baselines.