紧凑的共形子图
Compact Conformal Subgraphs
AI总结：
本文提出基于图的共形压缩框架，通过选择最小子图保留统计有效性并减少结构复杂度，实现高效共形预测与图压缩的结合，同时揭示了新的算法 regime。
摘要：
共形预测提供严格的、无分布的不确定性保证，但通常在结构领域如路由、规划或序列推荐中会产生过于庞大的预测集。我们引入了基于图的共形压缩框架，通过选择最小的子图来保持统计有效性并减少结构复杂度。我们将压缩定义为选择一个最小的子图，以捕捉指定比例的概率质量，并将其转化为超图中的加权最密集k子图问题，在子图具有大量边的比例情况下。我们设计了高效的近似算法，实现了常数因子的覆盖和大小权衡。关键的是，我们证明了我们的松弛满足单调性性质，这一性质源于与参数最小割的联系，从而保证了所需的嵌套性，以提供有效的共形保证。我们的结果一方面通过单调性将高效的共形预测与组合图压缩联系起来，为统计有效性和压缩或大小提供严格的保证。另一方面，它们也突显了一个不同于经典最密集k子图难度设置的算法领域，在该领域问题可以被高效近似。我们最后通过旅行规划和导航的模拟验证了我们的算法方法，并将其与自然基线进行比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
