Exponentially Consistent Low-Complexity Outlier Hypothesis Testing for Continuous Sequences

TL;DR

This paper introduces a new class of low-complexity, exponentially consistent tests for outlier detection in continuous sequences, improving the tradeoff between detection accuracy and computational efficiency over existing methods.

Contribution

It extends outlier hypothesis testing to continuous-valued sequences using a distribution-free MMD-based test, handling both known and unknown outlier counts with performance bounds.

Findings

Achieves exponential consistency with low complexity

Extends previous discrete sequence results to continuous data

Provides bounds on detection performance and error tradeoffs

Abstract

In this work, we revisit outlier hypothesis testing and propose exponentially consistent, low-complexity fixed-length tests that achieve a better tradeoff between detection performance and computational complexity than existing exhaustive-search methods. In this setting, the goal is to identify outlying sequences from a set of observed sequences, where most sequences are i.i.d. from a nominal distribution and outliers are i.i.d. from a different anomalous distribution. While prior work has primarily focused on discrete-valued sequences, we extend the results of Bu et al. (TSP 2019) to continuous-valued sequences and develop a distribution-free test based on the MMD metric. Our framework handles both known and unknown numbers of outliers. In the unknown-count case, we bound the detection performance and characterize the tradeoff among the exponential decay rates of three types of error probabilities. Finally, we quantify the performance penalty incurred when the number of outliers is unknown.