论文标题
在线联合拓扑识别和来自缺少数据的流的信号估算
Online Joint Topology Identification and Signal Estimation from Streams with Missing Data
论文作者
论文摘要
识别一组时间序列的拓扑对于预测，去索和数据完成等任务很有用。基于矢量自回旋（VAR）基于模型的拓扑结构捕获时间序列之间的依赖性，通常是根据观察到的时空数据推断出来的。当数据受噪声和/或丢失的样本影响时，拓扑识别和信号恢复（重建）任务必须共同执行。当i）基本拓扑是时间变化时，会出现其他挑战。这项研究提出了一种在线算法，以克服这些挑战在估计基于VAR模型的拓扑结构中，并且在每个迭代中具有恒定的复杂性，这使得对大数据方案变得有趣。不确定的近端在线梯度下降框架用于以动态遗憾的形式得出所提出的算法的性能保证。还提供了数值测试，显示了所提出的算法以在线方式跟踪丢失数据的时变拓扑的能力。
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.
