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.

This submission presents a "three-layer" Gaussian process for multiple time-series analysis: a layer for transforming the input, a layer for convolutional GP, and a layer for warping the outputs. This is a different "twist" or "favour" of the existing deep-GP model. Approximate inference is via the scalable version of variational inference using inducing points. The authors state that one main contribution is the "closed-form solution for the \Phi -statistics for the convolution kernel". Experiments on a real data set from two wind turbines demonstrates its effectiveness over three existing models in terms of test-log-likelihoods. [Quality] This is a quality work, with clear model, approximation and experimental results.

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 present a Bayesian extension to convolution processes which defines a representation between multiple functions by an embedding in a shared latent space. The proposed model allows for both arbitrary alignments of the inputs and and also non-parametric output warpings to transform the observations. This gives rise to multiple deep Gaussian process models connected via latent generating processes. We derive 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.