Change-Point Detection on Hierarchical Circadian Models

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 lowerdimensional 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.

Multinomial Sampling for Hierarchical Change-Point Detection

“…where the conditional distribution p(x t |z t ) is assumed to be fixed and p(z t |θ t ) is the new likelihood distribution over the latent variable z t , that can be either continuous or discrete. Similar ideas were previously explored in [4,7] as extensions of the BOCPD method, where only discrete z t variables were considered.…”

“…We introduce the hierarchical model in [4], where z t is a categorical r.v. or class, such that z t = {1, 2, .…”

“…where p(r t |r t−1 ) is the conditional prior that modulates how likely is to detect a new CP, that is r t = 0, given the previous run-length hypothesis r t−1 . The full development of the joint probability and the details of p(r t |r t−1 ) are explained in [4]. The predictive term Ψ (r) t is obtained as…”

“…Latent variable models are amenable to overcome the high-dimensionality issue. Under the assumption that changepoints lie on a lower-dimensional manifold, one can extend the BOCPD algorithm to accept surrogate mixture models [4]. The main drawback is that true latent class assignments are never observed but inferred, leading to introduce pseudoobservations.…”

Continual Learning for Infinite Hierarchical Change-Point Detection

“…To address the aforementioned issue, in [8] we presented a hierarchical probabilistic model based on latent classes, i.e., a mixture model. The CPD problem can be carried out directly on the lowerdimensional manifold, where the discrete latent variables lie.…”