从含缺失数据的流中进行在线联合拓扑识别与信号估计
Online Joint Topology Identification and Signal Estimation from Streams with Missing Data
AI总结：
针对含缺失数据的流式时间序列，本文提出一种每次迭代恒定复杂度的在线算法，联合完成基于VAR模型的时变拓扑识别与信号估计，并利用非精确近端在线梯度下降框架给出动态遗憾界性能保证。
摘要：
识别一组时间序列背后的拓扑结构对于预测、去噪和数据补全等任务十分有用。基于向量自回归（VAR）模型的拓扑能够刻画时间序列之间的依赖关系，通常从观测到的时空数据中推断得到。当数据受到噪声和/或缺失样本影响时，拓扑识别与信号恢复（重建）任务必须联合执行。当以下情况出现时还会带来额外挑战：i) 底层拓扑是时变的，ii) 数据按顺序依次到达，iii) 不允许任何延迟。本研究提出一种在线算法，以克服在估计基于VAR模型的拓扑时所面临的这些挑战，该算法每次迭代具有恒定复杂度，这使其对大数据场景具有吸引力。利用非精确近端在线梯度下降框架，以动态遗憾界的形式为所提算法推导出性能保证。文中还给出了数值测试，展示了所提算法在含缺失数据情况下以在线方式跟踪时变拓扑的能力。
英文摘要：
Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often inferred from observed spatio-temporal data. When data are affected by noise and/or missing samples, topology identification and signal recovery (reconstruction) tasks must be performed jointly. Additional challenges arise when i) the underlying topology is time-varying, ii) data become available sequentially, and iii) no delay is tolerated. This study proposes an online algorithm to overcome these challenges in estimating VAR model-based topologies, having constant complexity per iteration, which makes it interesting for big-data scenarios. The inexact proximal online gradient descent framework is used to derive a performance guarantee for the proposed algorithm, in the form of a dynamic regret bound. Numerical tests are also presented, showing the ability of the proposed algorithm to track time-varying topologies with missing data in an online fashion.
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。
