Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection
This addresses computational efficiency in universal outlying sequence detection, which is incremental as it builds on existing tests but offers linear complexity.
The paper tackles the problem of detecting outlying sequences among multiple sequences without prior knowledge of the underlying distributions, proposing distribution clustering-based tests that achieve exponential consistency with linear time complexity in the number of sequences.
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. 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.