Active Anomaly Detection in Heterogeneous Processes

TL;DR

This paper introduces a low-complexity, deterministic active inference strategy for anomaly detection in heterogeneous processes, achieving asymptotic optimality and improved finite-sample performance over traditional randomized tests.

Contribution

It proposes a novel deterministic testing method that matches Chernoff test asymptotic optimality with better finite-sample performance and lower computational complexity.

Findings

Deterministic test achieves asymptotic optimality similar to Chernoff test.

The proposed method performs better in finite regimes.

Lower computational complexity compared to existing methods.

Abstract

An active inference problem of detecting anomalies among heterogeneous processes is considered. At each time, a subset of processes can be probed. The objective is to design a sequential probing strategy that dynamically determines which processes to observe at each time and when to terminate the search so that the expected detection time is minimized under a constraint on the probability of misclassifying any process. This problem falls into the general setting of sequential design of experiments pioneered by Chernoff in 1959, in which a randomized strategy, referred to as the Chernoff test, was proposed and shown to be asymptotically optimal as the error probability approaches zero. For the problem considered in this paper, a low-complexity deterministic test is shown to enjoy the same asymptotic optimality while offering significantly better performance in the finite regime and faster convergence to the optimal rate function, especially when the number of processes is large. The computational complexity of the proposed test is also of a significantly lower order.