提出新方法MOSAIC，高效检测动态网络中的变化点。
MOSAIC: Minimax-Optimal Sparsity-Adaptive Inference for Change Points in Dynamic Networks
- 基于特征分解与信号筛选的检验方法，逼近理论最优性能。
- 理论证明可检测到稀疏变化，且误差仅含微小对数项。
- 适合分析具有低秩和稀疏变化特性的动态网络数据。
我们提出一种名为MOSAIC的新推断框架，用于检测具有低秩与稀疏变化结构的动态网络中的变化点。建立了检测边界的极小极大率，该率依赖于变化的稀疏性。随后设计了一种基于特征分解的检验方法，通过筛选信号逼近极小极大率，仅存在轻微对数损失。在实际应用中，采用新颖的残差技术调整理论检验，得到一个枢轴统计量，在零假设下依鞅中心极限定理收敛至标准正态分布，并在备择假设下达到全功效。此外，我们分析了无低秩结构的动态网络的极小极大检验边界，其结果几乎与高维均值向量变化点推断一致。通过多个模拟实验和真实数据应用验证了MOSAIC的有效性及理论结论。
原文摘要 · Abstract (English)
We propose a new inference framework, named MOSAIC, for change-point detection in dynamic networks with the simultaneous low-rank and sparse-change structure. We establish the minimax rate of detection boundary, which relies on the sparsity of changes. We then develop an eigen-decomposition-based test with screened signals that approaches the minimax rate in theory, with only a minor logarithmic loss. For practical implementation of MOSAIC, we adjust the theoretical test by a novel residual-based technique, resulting in a pivotal statistic that converges to a standard normal distribution via the martingale central limit theorem under the null hypothesis and achieves full power under the alternative hypothesis. We also analyze the minimax rate of testing boundary for dynamic networks without the low-rank structure, which almost aligns with the results in high-dimensional mean-vector change-point inference. We showcase the effectiveness of MOSAIC and verify our theoretical results with several simulation examples and a real data application.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。