Polynomial-Complexity, Exponentially Consistent Tests for Outlying Sequence Detection

We study an outlying sequence detection problem, in which there are $M$ sequences of samples out of which a small subset of outliers needs to be detected. A sequence is considered an outlier if the observations therein are generated by a distribution different from those generating the observations in the majority of sequences. In the universal setting, the goal is to identify all the outliers without any knowledge about the underlying generating distributions. In prior work, this problem was studied as a universal hypothesis testing problem, and a generalized likelihood (GL) test with high computational complexity was constructed and its asymptotic performance characterized. we novelly propose a test based on distribution clustering. Such a test is shown to be exponentially consistent and the time complexity is linear in the total number of sequences. Furthermore, our tests based on clustering are applicable to more general scenarios, e.g., when both the typical and outlier distributions forming clusters, our new tests is exponentially consistent, but the GL test is not even applicable.