Bayesian Alignments of Warped Multi-Output Gaussian Processes
This work addresses the challenge of aligning and analyzing dependent time series in real-world applications like wind energy, though it appears incremental as it builds on existing Gaussian process methods.
The authors tackled the problem of modeling nonlinear alignments in time series by proposing a Bayesian approach that uses latent shared information, applied to wind turbine sensor data to extract common structure from turbulent wind fields, achieving an interpretable functional decomposition.
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.