Second-Order Asymptotically Optimal Outlying Sequence Detection with Reject Option
作者：周琳 时间：2021年11月23日 21:16 点击数：
语言：English
发表会议：2021 IEEE Information Theory Workshop (ITW)
发表日期：2021年11月23日
摘要：
Motivated by practical machine learning applications, we revisit the outlying sequence detection problem (Li et al., TIT 2014) and derive fundamental limits of optimal detection when the reject option is allowed for outlying sequences. In the considered outlying sequence detection (OSD) problem, one is given multiple observed sequences, where all sequences are generated i.i.d. from a nominal distribution with at most one exception. The task is to discern the outlying sequence that is generated according to an anomalous distribution. In OSD, the nominal and anomalous distributions are unknown. In this paper, we consider the case where there is a reject option for the OSD, i.e., we reject the samples as insufficient for making a reliable decision (cf. Bartlett et al., JMLR 2008). We study the tradeoff among the probabilities of misclassification error, false alarm and false reject for tests that satisfy weak conditions on the rate of decrease of these error probabilities as a function of sequence length. We propose a second-order asymptotically optimal test that provides a finite sample approximation to the error probabilities.
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