  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.
