提出动态藤蔓耦合模型,捕捉时变高阶依赖关系。
Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions

- 用固定藤结构建模时序非高斯依赖,支持参数平滑与族切换路径。
- 通过截断藤对比检测到条件交互信号,在神经数据中可复现。
- 适合研究复杂系统中非配对依赖的演变,如脑区协同活动。
时间变化的依赖常通过动态相关或高斯图模型建模,但多变量系统可能在相关性稳定时仍因尾部行为、不对称性或条件结构变化而改变。我们提出动态藤蔓耦合(DVC),一种用于估计和诊断序列级非高斯依赖的时序藤蔓耦合框架。DVC 固定一个选定的藤结构以保证可比性;框架适用于 C-、D- 和 R-藤,实验采用固定根序的 C-藤。成对耦合状态通过平滑参数轨迹或时序正则化的族切换路径演化。主要诊断方法是将完整藤与匹配的1-截断版本进行留出比较,分离出第一层成对依赖的灵活性与高层条件项的贡献证据。在总体层面,该对比等于藤总相关性的高层成分;在有限样本中,作为预测诊断工具。在受控基准测试中,DVC 能检测学生分布自由度变化、Clayton到Gumbel的转换以及被高斯动态基线遗漏或混淆的周期性条件交互事件。高层得分在仅成对依赖的场景下接近零,在条件交互阶段上升。在Allen视觉行为Neuropixels数据上,DVC识别出一个跨分割可重复的时间索引高层信号,在所有留出切片中为正,而在去相关零模型下消失,表明跨脑区的同时依赖。因此,DVC 提供了一种灵活的时序耦合模型,并提供了可解释的检验方法,判断时序依赖变化是否为成对或条件型。
原文摘要 · Abstract (English)
Time-varying dependence is often modeled with dynamic correlations or Gaussian graphical models, but multivariate systems can change through tail behavior, asymmetry, or conditional structure even when correlations are nearly stable. We introduce Dynamic Vine Copulas (DVC), a temporal vine-copula framework for estimating and diagnosing sequence-wide non-Gaussian dependence. DVC fixes a chosen vine factorization for comparability; the framework applies to C-, D-, and R-vines, and our experiments use fixed-root-order C-vines. Pair-copula states evolve through smooth parameter trajectories or temporally regularized family-switching paths. The main diagnostic is a held-out comparison between a full vine and its matched 1-truncated version, which separates flexible first-tree pairwise dependence from evidence contributed by higher-tree conditional terms. At the population level, under a correct fixed vine and the simplifying assumption, this contrast equals the higher-tree component of a vine total-correlation decomposition; in finite samples, it is a predictive diagnostic. In controlled benchmarks, DVC detects Student-t degrees-of-freedom changes, Clayton-to-Gumbel switches, and recurrent conditional-interaction episodes missed or conflated by Gaussian dynamic baselines. The higher-tree score remains near zero in pairwise-only regimes and rises during conditional-interaction regimes. On Allen Visual Behavior Neuropixels data, DVC identifies a reproducible time-indexed higher-tree signal that is positive across held-out splits and vanishes under a decorrelated null, indicating simultaneous cross-area dependence. DVC therefore provides a flexible temporal copula model and an interpretable test of whether temporal dependence changes are pairwise or conditional.
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