Title: Bayesian Alignments of Warped Multi-Output Gaussian Processes,
Abstract: We propose a novel Bayesian approach to modelling nonlinear alignments of
time series based on latent shared information. We apply the method to the
real-world problem of finding common structure in the sensor data of wind
turbines introduced by the underlying latent and turbulent wind field. The
proposed model allows for both arbitrary alignments of the inputs and
non-parametric output warpings to transform the observations. This gives rise
to multiple deep Gaussian process models connected via latent generating
processes. We present an efficient variational approximation based on nested
variational compression and show how the model can be used to extract shared
information between dependent time series, recovering an interpretable
functional decomposition of the learning problem. We show results for an
artificial data set and real-world data of two wind turbines.