Active Learning for Multiple Change Point Detection in Non-stationary Time Series with Deep Gaussian Processes

TL;DR

The paper tackles offline multiple change point detection in non-stationary time series under costly data acquisition. It introduces a threefold framework that integrates Deep Gaussian Processes for flexible non-stationary modeling, spectral analysis via sliding window Fourier transforms, and an Active Learning-driven data acquisition strategy guided by a Spectral Change Detection Metric and spectral uncertainty. The core contributions are the Spectral Change Detection Metric (SCDM), a spectral-uncertainty aware Acquisition Function, and the demonstration that combining DGPs with spectral features improves MCP detection accuracy and sampling efficiency across synthetic and real-world datasets. The approach offers robust performance across diverse change patterns and noise levels, enabling efficient monitoring and decision-making in engineering and environmental contexts where data collection is expensive or intrusive.

Abstract

Multiple change point (MCP) detection in non-stationary time series is challenging due to the variety of underlying patterns. To address these challenges, we propose a novel algorithm that integrates Active Learning (AL) with Deep Gaussian Processes (DGPs) for robust MCP detection. Our method leverages spectral analysis to identify potential changes and employs AL to strategically select new sampling points for improved efficiency. By incorporating the modeling flexibility of DGPs with the change-identification capabilities of spectral methods, our approach adapts to diverse spectral change behaviors and effectively localizes multiple change points. Experiments on both simulated and real-world data demonstrate that our method outperforms existing techniques in terms of detection accuracy and sampling efficiency for non-stationary time series.

Figures (4)

• Figure 1: Examples of Change Patterns in Stochastic Time Series. Each subplot illustrates a unique structural change occurring at the middle, denoted by a grey dashed vertical line.
• Figure 2: Architecture of a DGP. Each layer $L$ corresponds to a $\text{GP}_l$ with latent function $f^l$ and inducing variables $\mathbf{Z}^l$, $\mathbf{U}^l$. The input to each layer is the output from the previous layer, and the model represents a nested composition $\mathbf{F}^l = f^l(f^{l-1}(\dots f^1(\mathbf{X})))$.
• Figure 3: Flowchart of Proposed Method. The methodology is achieved via three main steps: (1) DGP modeling: fit the non-stationary time series data; (2) active sampling: select extra data points based on spectral distance metrics and uncertainty estimates; (3) change point identification: estimate change points through spectral analysis.
• Figure 4: DGP mean and variance predictions for the Well log dataset with an AF explore-exploit parameter $\beta$ = 0.75. Red crosses represent the initial training points, while green circles are the points selected during AL iterations 5 and 10, as shown in (a) and (b). Each iteration uses a batch size of 5.