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.

翻译：共形预测提供了严格且无分布的不确定性保证，但在路由、规划或序列推荐等结构化领域中，其产生的预测集往往过大而难以实际应用。本文提出“基于图的共形压缩”框架，用于构建紧致的子图，在保持统计有效性的同时降低结构复杂性。我们将压缩问题形式化为选择能捕获规定概率质量分数的最小子图，并将其归约为超图中加权版最稠密$k$-子图问题，其中子图需包含较大比例的边。我们设计了高效的近似算法，可实现覆盖率与规模之间的恒定因子权衡。关键的是，我们证明了所提出的松弛方法满足单调性——这一性质源于与参数最小割的联系，从而保证了有效共形保证所需的嵌套性。一方面，我们的研究通过单调性将高效共形预测与组合图压缩相连接，为统计有效性和压缩率（或规模）同时提供严格保证；另一方面，结果也揭示了一个区别于经典最稠密-$k$-子图困难性设定的算法机制，使得该问题可被高效近似求解。最后，我们通过行程规划和导航的仿真实验验证了所提算法，并与自然基线方法进行了对比。