论文标题
使用Wasserstein歧义集的最小值最快的最快更改检测
Minimax Robust Quickest Change Detection using Wasserstein Ambiguity Sets
论文作者
论文摘要
我们研究未知前后分布的最快变化检测。为了处理数据生成分布中的不确定性，我们根据Wasserstein距离制定了两个数据驱动的歧义集，而没有任何参数假设。在最小有利的分布下，最小值鲁棒测试被构造为Cusum测试，这是歧义集中的一对代表性分布。我们表明，最小鲁棒测试可以以易于处理的方式获得，并且在渐近上是最佳的。我们研究了对现有方法的强大测试的有效性，包括基于KL差异的歧义集中的广义似然比测试和可靠测试。
We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance, without any parametric assumptions. The minimax robust test is constructed as the CUSUM test under least favorable distributions, a representative pair of distributions in the ambiguity sets. We show that the minimax robust test can be obtained in a tractable way and is asymptotically optimal. We investigate the effectiveness of the proposed robust test over existing methods, including the generalized likelihood ratio test and the robust test under KL divergence based ambiguity sets.
