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 % We set this for hyperref
 \title{Dynamic Dirichlet Deep GP}
 \author{\href{mailto:markus.kaiser@siemens.com}{Markus Kaiser}}

 \author{
 % Markus Kaiser\\
 % Siemens AG\\
 % Technical University of Munich\\
 % \texttt{markus.kaiser@siemens.com}\\
 % \And
 % Clemens Otte\\
 % Siemens AG\\
 % \texttt{clemens.otte@siemens.com}\\
 % \And
 % Thomas Runkler\\
 % Siemens AG\\
 % Technical University of Munich\\
 % \texttt{thomas.runkler@siemens.com}\\
 % \And
 % Carl Henrik Ek\\
 % University of Bristol\\
 % \texttt{carlhenrik.ek@bristol.ac.uk}\\
 % NOTE: Fix metadata.
 Anonymous\\
 }

 \begin{document}
 \maketitle

 \begin{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 realworld 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 nonparametric 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 realworld data of two wind turbines.
 \end{abstract}


 \section{Introduction}
 Many realworld systems are inherently hierarchical and connected.
 Ideally, a machine learning method should model and recognize such dependencies.
 Take wind power production, which is one of the major providers for renewable energy today, as an example:
 To optimize the efficiency of a wind turbine the speed and pitch have to be controlled according to the local wind conditions (speed and direction).
 In a wind farm turbines are typically equipped with sensors for wind speed and direction.
 The goal is to use these sensor data to produce accurate estimates and forecasts of the wind conditions at every turbine in the farm.
 For the ideal case of a homogeneous and very slowly changing wind field, the wind conditions at each geometrical position in a wind farm can be estimated using the propagation times (time warps) computed from geometry, wind speed, and direction \parencite{soleimanzadeh_controller_2011,bitar_coordinated_2013,schepers_improved_2007}.
 In the real world, however, wind fields are not homogeneous, exhibit global and local turbulences, and interfere with the turbines and the terrain inside and outside the farm and further, breaking sensors can lead to data loss.
 This makes it extremely difficult to construct accurate analytical models of wind propagation in a farm.
 Also, standard approaches for extracting such information from data, e.g.\ generalized time warping \parencite{zhou_generalized_2012}, fail at this task because they rely on a high signal to noise ratio.
 Instead, we want to construct Bayesian nonlinear dynamic data based models for wind conditions and warpings which handle the stochastic nature of the system in a principled manner.

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 \end{document}
