Distributional Change Point Detection via Dense ReLU Networks

Music City Center 

We study the problem of detecting changes in conditional distributions over time, where the relationship between inputs and responses shifts at unknown time points, referred to as change points. The conditional distributions are assumed to belong to a structured class of hierarchical models and remain piecewise constant between change points. Our objective is to estimate the locations of these changes and analyze the conditions under which they can be reliably detected. To achieve such a task, a novel method, Deep Distributional Change Point Detection, is introduced. It combines a Dense ReLU network-based estimation algorithm with a Seeded Binary Segmentation procedure to efficiently identify and localize changes in conditional distributions. Our theoretical analysis examines the impact of varying model parameters as the number of observations increases, including the minimum spacing between consecutive change points and the smallest detectable shift in distributions. We establish fundamental limits on localization accuracy and derive the minimum signal strength required for consistent detection. Extensive numerical experiments demonstrate the effectiveness of the proposed method.

Change Point

Dense ReLU Network

CUSUM estimator

Seeded Binary Segmentation 

Section on Nonparametric Statistics