Change Detection via Affine and Quadratic Detectors

TL;DR

This paper applies convex optimization-based hypothesis testing to develop sequential change detection methods for linear dynamical systems with noisy observations, distinguishing between nuisance inputs and nontrivial signals.

Contribution

It introduces computation-friendly, near-optimal sequential decision rules for change detection using affine and quadratic detectors within a convex optimization framework.

Findings

Developed near-optimal sequential detection rules.

Applicable to systems with sub-Gaussian noise.

Effective in distinguishing nuisance from nontrivial signals.

Abstract

The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of Statistics 10:2204--2242, 2016. Namely, we consider the Change Detection problem as follows: given an evolving in time noisy observations of outputs of a discrete-time linear dynamical system, we intend to decide, in a sequential fashion, on the null hypothesis stating that the input to the system is a nuisance, vs. the alternative stating that the input is a "nontrivial signal," with both the nuisances and the nontrivial signals modeled as inputs belonging to finite unions of some given convex sets. Assuming the observation noises zero mean sub-Gaussian, we develop "computation-friendly" sequential decision rules and demonstrate that in our context these rules are provably near-optimal.