发表机构
Delft University of Technology（代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对时变单纯复形跟踪问题，提出一种考虑包含性质的非线性状态空间模型，通过闭包感知的马尔可夫生成模型和约束伪测量，结合扩展卡尔曼滤波等方法，实现动态单纯复形的有效估计。
AI 中文摘要
单纯复形（SCs）将图扩展以表示高阶交互，但通过包含性质将其单纯形层级耦合在一起。虽然静态单纯复形推断是一个新兴的研究方向，但跟踪时变单纯复形在很大程度上仍未得到探索。跟踪单纯复形的一个核心挑战是考虑包含性质。为此，我们构建了一个针对单纯复形定制的非线性状态空间模型。在预测方面，我们引入了一个闭包感知的马尔可夫生成模型，其条件均值保持单纯形包含性，其协方差捕捉边-三角形依赖关系。在修正方面，我们将包含约束编码为非线性伪测量，使约束能够同时影响状态和协方差更新。我们通过标准扩展卡尔曼滤波器、迭代扩展卡尔曼滤波器和拉普拉斯近似研究了这些测量的逐渐丰富的处理方法。实验证明了利用所提出的动力学和约束信息的好处。
英文摘要
Simplicial complexes (SCs) extend graphs to represent higher-order interactions, but couple their simplex levels through the inclusion property. While static SC inference is an emerging research direction, tracking time-varying SCs remains largely unexplored. A central challenge in tracking SCs is to account for the inclusion property. To this end, we build a nonlinear state-space model tailored to SCs. For prediction, we introduce a closure-aware Markov generation model whose conditional mean preserves simplicial inclusion and whose covariance captures edge-triangle dependencies. For correction, we encode inclusion constraints as nonlinear pseudo-measurements, allowing the constraints to inform both the state and covariance updates. We investigate progressively richer treatments of these measurements through a standard extended Kalman filter, an iterated extended Kalman filter, and a Laplace approximation. Experiments then demonstrate the benefits of exploiting the proposed dynamics and constraint information.
CommentsSubmitted to ICAASP 2027
