We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions are not tractable as they rely on some minimax and robust variant of the objective. As a consequence, change points might be detected too late for practical applications (in economics, health care or maintenance for instance). Available constant complexity techniques typically solve a relaxed version of the problem, deeply relying on very specific probability distributions and/or some very precise additional knowledge. We consider a totally different approach that leverages the theoretical asymptotic properties of optimal solutions to derive a new scalable approximate algorithm with near optimal performance that runs~in~$\mathcal{O}(1)$, adapted to even more complex Markovian settings.
翻译:我们认为,在变化前和变化后分布的参数都不为人知的情况下,最快速的变化检测问题最为突出,这使得无法使用经典的简单假设测试。如果没有额外的假设,最佳解决方案就无法推进,因为它们依赖于某些微型和稳健的目标变量。因此,对实际应用(例如经济学、医疗保健或维护)而言,检测到变化点可能为时太晚。 现有的常态复杂技术通常能解决问题的一个宽松版本,深深依赖非常具体的概率分布和/或一些非常精确的额外知识。 我们考虑一种完全不同的方法,利用最佳解决方案的理论零碎特性来产生一种几乎最佳的可缩放近乎最佳的算法,这种算法运行到~$\mathcal{O}(1)$,适应更复杂的马尔科维安环境。