从全局到局部关联：统计推断的几何分解
From Global to Local Correlation: Geometric Decomposition of Statistical Inference
AI总结：
针对高维数据全局关联方法遗漏亚群异质模式的问题，提出基于黎曼图的几何分解框架，通过两种局部划分策略实现更精准的统计推断与多模态整合。
摘要：
当不同亚群间的关联存在差异时，理解高维数据中的特征-结果关联仍是一项挑战，而假设存在全局关联的标准方法会遗漏依赖上下文的模式，降低统计功效与可解释性。我们提出了一种几何分解框架，提供两种策略将推断问题拆解为在数据衍生的黎曼图上开展的区域分析。梯度流分解采用经路径单调性验证的离散莫尔斯理论，将样本划分为结果呈现单调行为的梯度流单元。共单调性分解利用顶点级系数给出经典皮尔逊相关的上下文适配版本：这些系数衡量结果与特征间、或特征对间基于边的方向一致性，将样本嵌入到关联空间中。这类嵌入会生成黎曼k近邻图，在该图上双聚类可识别共单调性单元（相干区域）与特征模块，该方法可自然扩展至多特征集的多模态整合场景。两种策略可独立或联合使用，通过贝叶斯后验采样提供可信区间。
英文摘要：
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical power and interpretability. We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses on data-derived Riemannian graphs. Gradient flow decomposition uses path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior. Co-monotonicity decomposition utilizes vertex-level coefficients that provide context-dependent versions of the classical Pearson correlation: these coefficients measure edge-based directional concordance between outcome and features, or between feature pairs, defining embeddings of samples into association space. These embeddings induce Riemannian k-NN graphs on which biclustering identifies co-monotonicity cells (coherent regions) and feature modules. This extends naturally to multi-modal integration across multiple feature sets. Both strategies apply independently or jointly, with Bayesian posterior sampling providing credible intervals.
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。
