Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection

The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequences. In the universal setting, we are interested in identifying all the outlying sequences without knowing the underlying generating distributions. We consider the outlying sequence detection problem in three different scenarios: first, known number of outlying sequences; second, unknown number of identical outlying sequences; and finally, typical and outlying distributions forming clusters. In this paper, a class of tests based on distribution clustering is proposed. These tests are shown to be exponentially consistent with linear time complexity in $M$. Numerical results demonstrate that our clustering-based tests achieve similar performance to existing tests, while being considerably more computationally efficient.