基于凸优化的鲁棒序列变点检测
Robust Sequential Change-Point Detection by Convex Optimization
摘要：
我们解决了计算的挑战，找到强大的顺序变点检测程序时，前和后的变化分布不完全指定。早期的工作[veeravalli 1994]和[Unnikrishnan 2011]建立了鲁棒程序的一般条件，其中包括找到一对最不利的分布（LFD）。然而，在多维设置中，很难通过计算找到这样的LFD。我们提出了一种基于凸优化的方法，解决了这个问题时，分布是高斯未知参数从预先指定的不确定性集。我们还建立了我们的鲁棒程序的理论性质，数值例子表明其良好的性能。
英文摘要：
We address the computational challenge of finding the robust sequential change-point detection procedures when the pre- and post-change distributions are not completely specified. Earlier works [veeravalli 1994] and [Unnikrishnan 2011] establish the general conditions for robust procedures which include finding a pair of least favorable distributions (LFDs). However, in the multi-dimensional setting, it is hard to find such LFDs computationally. We present a method based on convex optimization that addresses this issue when the distributions are Gaussian with unknown parameters from pre-specified uncertainty sets. We also establish theoretical properties of our robust procedures, and numerical examples demonstrate their good performance.
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