Problem
Research questions and friction points this paper is trying to address.
stratified sampling
redistricting plans
phase space
balanced graph partitions
candidate strata
Towards stratified sampling for redistricting plans
🤖 AI Summary
该研究针对选区重划中的高维组合问题，通过构建和诊断具有适当覆盖和重叠的候选层来实现分层抽样，使用聚类方法形成计划层面的'单词'。
📝 Abstract
Rapid algorithmic developments have accelerated the sampling of redistricting ensembles (balanced graph partitions), yet evaluating rare events and sampling complex target measures remains a core challenge due to the high-dimensional and combinatorial nature of the phase space. We address a prerequisite for stratified sampling on this space: constructing and diagnosing candidate strata with suitable coverage and overlap. We build a grammar on observed plans by clustering districts into representative ``letters'' and using them to form plan-level ``words.'' A partition of unity over these words gives a soft assignment of plans to strata and allows us to estimate stratum masses and an overlap-induced flux matrix. We demonstrate this computational pipeline using real-world congressional redistricting data from Connecticut and examine how strata learned from one target distribution behave under related distributions. The resulting construction provides a foundation for future stratified sampling on spaces of redistricting plans or balanced graph partitions. We do not implement a complete stratified sampler here; evaluating whether the proposed strata improve sampling efficiency or reduce estimator variance is left for future work.
Innovation
Methods, ideas, or system contributions that make the work stand out.
stratified sampling
redistricting plans
balanced graph partitions
partition of unity
flux matrix
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