Dynamical Wasserstein Barycenters for Time-series Modeling

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary pure-state'' periods as well as transition periods between adjacent segments, such as a gradual slowdown between running and walking. However, most prior work assumes instantaneous transitions between pure discrete states. We propose a dynamical Wasserstein barycentric (DWB) model that estimates the system state over time as well as the data-generating distributions of pure states in an unsupervised manner. Our model assumes each pure state generates data from a multivariate normal distribution, and characterizes transitions between states via displacement-interpolation specified by the Wasserstein barycenter.