Change-Point Detection on Hierarchical Circadian Models

TL;DR

This paper introduces a hierarchical, latent-variable-based change-point detection method for high-dimensional, heterogeneous, and periodic data, with applications in behavioral analysis and psychiatric relapse detection.

Contribution

It proposes a novel hierarchical model with periodic covariance functions that effectively detects change-points in complex, real-world data while handling missing values and heterogeneity.

Findings

Successfully detects behavioral change-points in smartphone data

Robust to missing data and heterogeneity in observations

Validated on synthetic and real-world datasets

Abstract

This paper addresses the problem of change-point detection on sequences of high-dimensional and heterogeneous observations, which also possess a periodic temporal structure. Due to the dimensionality problem, when the time between change-points is on the order of the dimension of the model parameters, drifts in the underlying distribution can be misidentified as changes. To overcome this limitation, we assume that the observations lie in a lower-dimensional manifold that admits a latent variable representation. In particular, we propose a hierarchical model that is computationally feasible, widely applicable to heterogeneous data and robust to missing instances. Additionally, the observations' periodic dependencies are captured by non-stationary periodic covariance functions. The proposed technique is particularly fitted to (and motivated by) the problem of detecting changes in human behavior using smartphones and its application to relapse detection in psychiatric patients. Finally, we validate the technique on synthetic examples and we demonstrate its utility in the detection of behavioral changes using real data acquired by smartphones.