Sequential Nonparametric Detection of Anomalous Data Streams

Abstract

We study a nonparametric search problem to detect $L$ anomalous streams from a finite set of $ S$ data streams. The $L$ anomalous streams are real-valued independent and identically distributed (i.i.d.) sequences drawn from the distribution $ q$ , while the remaining $S-L$ data streams are i.i.d. sequences drawn from the distribution $ p$ . The distributions $ p$ and $ q$ are assumed to be arbitrary and unknown , but distinct. We consider two cases: one where $L = 1$ , and the other where $0 \leq L \leq A$ . In both cases, we propose universal distribution-free sequential tests that are consistent. For the first case, we also: (1) show that the test is universally exponentially consistent and stops in finite time almost surely, and (2) bound the limiting growth rate of the expected stopping time as the probability of error decreases to zero. Simulations show that the performance of the proposed test is better than that of the fixed sample size test.