REAMP: A Stochastic Resonance Approach for Multi-Change Point Detection in High-Dimensional Data

TL;DR

REAMP addresses the challenge of detecting multiple change points in high-dimensional data, including changes in higher-order moments, by marrying optimal transport with stochastic resonance. It employs a two-stage dimension reduction via Earth Mover's Distance and Shortest Hamiltonian Paths to build a graph-based count statistic, and introduces a stochastic resonance step with randomized Beta priors to generate a cloud of candidate change points, refined by a double sharpening procedure. The paper proves asymptotic consistency of the resonance estimator under a set of assumptions and demonstrates through simulations that REAMP outperforms state-of-the-art methods, especially when mean and variance shift simultaneously. In a real-data application to time-lapse embryo monitoring, REAMP provides accurate detection and intuitive visualization of cell division stages, suggesting broad applicability.

Abstract

Detecting multiple structural breaks in high-dimensional data remains a challenge, particularly when changes occur in higher-order moments or within complex manifold structures. In this paper, we propose REAMP (Resonance-Enhanced Analysis of Multi-change Points), a novel framework that integrates optimal transport theory with the physical principles of stochastic resonance. By utilizing a two-stage dimension reduction via the Earth Movers Distance (EMD) and Shortest Hamiltonian Paths (SHP), we map high-dimensional observations onto a graph-based count statistic. To overcome the locality constraints of traditional search algorithms, we implement a stochastic resonance system that utilizes randomized Beta-density priors to vibrate the objective function. This process allows multiple change points to resonate as global minima across iterative simulations, generating a candidate point cloud. A double-sharpening procedure is then applied to these candidates to pinpoint precise change point locations. We establish the asymptotic consistency of the resonance estimator and demonstrate through simulations that REAMP outperforms state-of-the-art methods, especially in scenarios involving simultaneous mean and variance shifts. The practical utility of the method is further validated through an application to time-lapse embryo monitoring, where REAMP provides both accurate detection and intuitive visualization of cell division stages.

Figures (5)

• Figure 1: Plot of $x_{\text{amp}}/(A_{\text{amp}}/K)$ with maximum at $\eta=\sqrt{1-2\zeta^2}$.
• Figure 2: Comparisons between the ground Euclidean distance and the EMD with the ground Euclidean distance.
• Figure 3: Comparison of REMAP statistics for detecting a variance shift. (Top Right) ED+MST fails, exhibiting spurious resonances. (Bottom Right) EMD improves MST performance, successfully resolving the peak. (Left Column) SHP-based statistics (ED and EMD) consistently isolate the change point with high precision, demonstrating superior power in high dimensions.
• Figure 4: Histogram and sharpening curve of $T_n(a, b)$ and estimated change points at 20, 50, and 75.
• Figure 5: Histogram and sharpening curve for $T_n(a, b)$ with estimated change points identified at frames 23, 192, and 268.