MuRAL-CPD: Active Learning for Multiresolution Change Point Detection

TL;DR

MuRAL-CPD tackles time-series change point detection under limited supervision by embedding an active learning loop into a wavelet-based multiresolution CPD backbone. The method leverages Multilevel Discrete Wavelet Decomposition to produce scale-aware discrepancy scores, which are linearly combined and sharpened by a prominence transform, with a learnable threshold guiding CP detection. User feedback optimizes the resolution weights and the detection threshold via a loss based on the F1 score, enabling rapid, task-specific adaptation without a separate supervised model. Experiments across HAR, PM, and BT datasets show competitive performance with state-of-the-art semi-supervised methods, particularly when supervision is scarce, and ablations highlight the importance of threshold initialization, query frequency, and an initial warm-up phase for robust learning.

Abstract

Change Point Detection (CPD) is a critical task in time series analysis, aiming to identify moments when the underlying data-generating process shifts. Traditional CPD methods often rely on unsupervised techniques, which lack adaptability to task-specific definitions of change and cannot benefit from user knowledge. To address these limitations, we propose MuRAL-CPD, a novel semi-supervised method that integrates active learning into a multiresolution CPD algorithm. MuRAL-CPD leverages a wavelet-based multiresolution decomposition to detect changes across multiple temporal scales and incorporates user feedback to iteratively optimize key hyperparameters. This interaction enables the model to align its notion of change with that of the user, improving both accuracy and interpretability. Our experimental results on several real-world datasets show the effectiveness of MuRAL-CPD against state-of-the-art methods, particularly in scenarios where minimal supervision is available.

Figures (7)

• Figure 1: Overview of the MuR-CPD algorithm. The input time series undergoes a Multilevel Wavelet Decomposition to extract multiresolution subbands. We compute discrepancy scores on each subband using a sliding window approach, followed by resampling to obtain feature vectors aligned with the original time index. Then we aggregate the features by a linear combination and apply the prominence function $\pi$ to highlight peaks, and change points are detected by applying a tunable decision threshold.
• Figure 2: The sorted score function $\gamma(t)$ plotted against the normalized index $t\in[0,1]$. The piecewise linear curve exhibits a steep initial drop followed by a gradual tail. The elbow point at $t\approx0.10$ (yellow circle) corresponds to the maximum curvature of $\gamma(t)$. Dashed lines project this point horizontally to $\zeta_0\approx0.90$ on the $\gamma$‐axis and vertically to $t$ on the $t$‐axis; $\zeta_0$ is selected as the initial decision threshold.
• Figure 3: Comparison between F1-scores achieved by ICPD and MuRAL-CPD on benchmark datasets across 10 repetitions. Solid lines represent the mean values across 10 repetitions, while shaded regions indicate the standard deviation across these repetitions.
• Figure 4: Evolution of F1-score, precision, and recall as a function of the number of user queries on the USC-HAD dataset using MuRAL-CPD. Solid lines represent the mean values across 5 USC-HAD sequences, each repeated 10 times, while shaded regions indicate the standard deviation across these repetitions.
• Figure 5: Comparison between MuRAL-CPD and its ablated variant MuRAL-CPD-Max under different threshold initialization strategies on the Honeybee Dance dataset. While MuRAL-CPD benefits from a more informed threshold initialization and achieves better early performance, both methods converge to similar F1-scores after approximately 25 queries. Solid lines represent the mean across 10 runs and 6 dataset while shaded areas represent the standard deviation across those repetitions.

Theorems & Definitions (2)

• Proposition 1
• proof