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

TL;DR

This paper introduces a new class of distribution clustering-based tests for universal outlying sequence detection that are both exponentially consistent and have linear time complexity, improving computational efficiency.

Contribution

The paper proposes a novel clustering-based testing method for outlier detection that is both universally applicable and computationally efficient, with proven exponential consistency.

Findings

Tests are exponentially consistent.

Achieve linear time complexity in the number of sequences.

Performance comparable to existing methods.

Abstract

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.