Doubly-online change- point detection for monitoring health status during sport activities

We provide an online framework for analyzing data recorded by smart watches during running activities. In particular, we focus on identifying vari- ations in the behavior of one or more measurements caused by changes in physical condition, such as physical discomfort, periods of prolonged de- training, or even the malfunction of measuring devices. Our framework con- siders data as a sequence of running activities represented by multivariate time series of physical and biometric data. We combine classical changepoint detection models with an unknown number of components with Gaussian state space models to detect distributional changes between a sequence of activities. The model considers multiple sources of dependence due to the se- quential nature of subsequent activities, the autocorrelation structure within each activity, and the contemporaneous dependence between different vari- ables. We provide an online Expectation-Maximization (EM) algorithm in- volving a sequential Monte Carlo (SMC) approximation of changepoint pre- dicted probabilities. As a byproduct of our model assumptions, our proposed approach processes sequences of multivariate time series in a doubly-online framework. While classical changepoint models detect changes between sub- sequent activities, the state space framework coupled with the online EM al- gorithm provides the additional benefit of estimating the real-time probability that a current activity is a changepoint.