发表机构
Jeju National University; NAVI Hyper-Tropicalization Research Institute, Jeju National University（济州国立大学; 济州国立大学 NAVI超热带化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出量子互信息统计量，用于检测时间序列中不受边缘分布漂移影响的依赖结构变点，在模拟数据和韩国气象观测数据上均展现出更优的检测性能。
AI 中文摘要
检测多元时间序列两个分量之间的依赖关系何时发生变化，同时边缘分布自由漂移，需要一种特定于依赖关系的统计量。我们将推断对象取为密度算子，即秩为的单位范数随机傅里叶特征的迹归一化二阶矩，而非概率分布。部分迹可精确恢复边缘算子，因此冯·诺依曼熵会产生量子互信息（QMI）统计量，该统计量由小矩阵的前缀和计算得出，无需密度估计、矩阵求逆或调优参数。我们开发了其所需的推断：一种分段可分代价，驱动惩罚最优划分，其分裂增益为 Holevo 信息；通过联合成对置换进行有限样本精确校准，针对序列依赖的序列采用块置换形式，以及一种精确、可证明一致的可交换性诊断，用于在两者间进行选择。我们还证明了加权卡方边界定律，针对基于秩的统计量，其边界在段长度而非其平方根处，且计算结果完全一致。在500次重复实验中，QMI检测非线性、无相关依赖变化的功效，比同一秩上的希尔伯特-施密特独立准则、距离相关、斯皮尔曼及经验copula统计量至少高15个百分点（只要任一统计量能检测到该变化）。在边缘漂移下，QMI的虚警率保持接近标称值，而经验copula统计量达到0.87。对八年每小时的韩国气象观测数据，两阶段分段与验证程序发现了超出随机预期的依赖变化候选（27个中有5个p≤0.05，而预期为1.4个）；第二阶段将其中一个验证为纯耦合变化，并将8个重新分类为边缘驱动的变化。
英文摘要
Dependence can change between variable blocks without changing correlation; serial dependence complicates calibration. We propose DOMIC, a rank-based detector using density-operator mutual information (DOMI). Unit-norm random features make sample-level partial traces exact, so prefix sums compute segment statistics at per-split cost independent of segment length; a Gram form uses the exact kernel. Permutation tests are finite-sample exact under pair or block exchangeability for windows and schemes fixed in advance; validity after data-driven scheme selection is unproved. For i.i.d. pairs with feature dimension, frequency draw and bandwidth fixed, we prove a weighted chi-square limit at independence for the rank-based random-feature statistic. An additive entropy cost with Holevo gains drives segmentation. DOMI attains higher localised power than rank, copula, kernel and distance baselines in most non-Gaussian and correlation-free settings; the Gram form leads or ties in all 16 non-Gaussian settings where any statistic exceeds 0.10. On a three-break benchmark, Holevo partitioning returns exactly three breaks in 47.5% of replicates, against at most 19% for calibrated baselines. Block-calibrated primary scans reject in all three pre-specified pairs of a US financial panel, with strongest stage-two evidence for stocks and Treasury yields. One of 27 weather candidates passes the multiplicity-corrected re-test; candidate selection is unadjusted.
Comments14 pages main text and 29 pages of supplementary material (proofs and additional experiments) in one file. Code and outputs: https://github.com/yunam-seo/domic-changepoint
