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\documentclass[
compress,
11pt,
aspectratio=1610,
c
]{beamer}
% Standalone
\usepackage{currfile}
\usepackage{standalone}
\usepackage{xstring} % standalone path magic
% Math
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\mathtoolsset{showonlyrefs,showmanualtags}
\usepackage{xfrac}
% Table
\usepackage{etoolbox}
\robustify\bfseries
\usepackage{colortbl}
\usepackage{booktabs}
\usepackage{tabularx}
\usepackage{siunitx}
% Theme
\usetheme{metropolis}
\usecolortheme{metropolis-siemens}
\metroset{block=fill}
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% NOTE(mrksr): Show overlay number on multi-page frames
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% Babel
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\usepackage{csquotes}
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% Figures
\providecommand{\figurepath}{figures}
\input{abbreviations.tex}
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% Bibliography
\usepackage[style=authoryear, backend=biber, url=false]{biblatex}
\addbibresource{../zotero_export.bib}
\addbibresource{../additional.bib}
\title{Data Association with Gaussian Processes}
\date{September 17, 2019}
\author{%
Markus Kaiser,
Clemens Otte,
Thomas A. Runkler,
Carl Henrik Ek
\texorpdfstring{\\}{, }
\href{mailto:markus.kaiser@siemens.com}{markus.kaiser@siemens.com}
}
\institute{%
Siemens AG,
Technical University of Munich,
University of Bristol
}
\titlegraphic{%
\hfill
\includegraphics[height=1cm]{bristol.pdf}
\quad
\includegraphics[height=1cm]{tum.pdf}
\quad
\includegraphics[height=1cm]{siemens_claim.pdf}
}
% \includeonlyframes{summary}
\begin{document}
\maketitle
\begin{frame}[label=noise_separation]{Noise Separation}
\centering
\includestandalonewithpath{figures/noise_separation}
\end{frame}
\begin{frame}[label=multimodal_data]{Multimodal data}
\centering
\includestandalonewithpath{figures/semi_bimodal}
\end{frame}
\begin{frame}[label=graphical_model]{Graphical Model of DAGP}
\centering
\includestandalonewithpath{figures/graphical_model_dagp}
\end{frame}
\begin{frame}<3-5,7>[label=wetchicken]{Wet-Chicken Benchmark\footcite{tresp_wet_1994,hans_efficient_2009}}
\centering
\includestandalonewithpath{figures/wetchicken}
\end{frame}
\begin{frame}[label=dynamics_posterior]{Multimodal System Dynamics\footcite{kaiser_interpretable_2019}}
\centering
\includestandalonewithpath{figures/dynamics_posterior_cut}
\end{frame}
\begin{frame}[label=policy]{Conservative Policy Training}
\centering
\begin{columns}[T]
\begin{column}{.45\textwidth}
\centering
\includestandalone{figures/policy_quiver}
\begin{align}
\Fun*{R}{x, y} = x
\end{align}
22\% drop rate
\end{column}
\begin{column}{.45\textwidth}
\centering
\uncover<2>{
\includestandalone{figures/conservative_policy_quiver}
\begin{align}
\Fun*{R^\prime}{x, y} = \Fun*{R}{x, y} - 5 \cdot \Prob{\text{drop} \given x, y}
\end{align}
19\% drop rate
}
\end{column}
\end{columns}
\end{frame}
\begin{frame}[label=summary]{Data Association with Gaussian Processes}
\medskip
\begin{block}{Model for multimodal data}
\vspace{1ex}
\begin{columns}[c]
\begin{column}[c]{.5\textwidth}
\begin{itemize}
\item Separate models per mode
\item Predictive Associations
\item Scalable inference
\end{itemize}
\end{column}
\begin{column}[c]{.475\textwidth}
\centering
\includestandalonewithpath{figures/graphical_model_dagp_tiny}
\end{column}
\end{columns}
\end{block}
%
\begin{block}{Informed decision making}
\begin{columns}[c]
\begin{column}[c]{.5\textwidth}
\begin{itemize}
\item Hierarchical priors
\item Interpretable sub-models
\item Stochastic systems
\end{itemize}
\end{column}
\begin{column}[c]{.475\textwidth}
\centering
\includestandalonewithpath{figures/policy_quiver_tiny}
\end{column}
\end{columns}
\end{block}
\centering
\vspace{-1ex}
Markus Kaiser --- \href{https://mrksr.de}{mrksr.de}
\end{frame}
\appendix
\nocite{kaiser_data_2018}
\begin{frame}[label=bibliography]
\printbibliography
\end{frame}
\begin{frame}[label=variational_bound]{Variational Bound}
\begin{align}
\Ell_{\text{DAGP}}
&= \Moment*{\E_{\Variat*{\mat{F}, \mat{\alpha}, \mat{U}}}}{\log\frac{\Prob*{\mat{Y}, \mat{A}, \mat{F}, \mat{\alpha}, \mat{U} \given \mat{X}}}{\Variat*{\mat{F}, \mat{\alpha}, \mat{U}}}} \\
&= \sum_{n=1}^N \Moment*{\E_{\Variat*{\mat{f_n}}}}{\log \Prob*{\mat{y_n} \given \mat{f_n}, \mat{a_n}}}
+ \sum_{n=1}^N \Moment*{\E_{\Variat*{\mat{\alpha_n}}}}{\log \Prob*{\mat{a_n} \given \mat{\alpha_n}}} \\
&\quad - \sum_{k=1}^K \KL*{\Variat*{\mat{u^{\pix{k}}}}}{\Prob*{\mat{u^{\pix{k}}} \given \mat{Z^{\pix{k}}}}}
- \sum_{k=1}^K \KL*{\Variat*{\mat{u_\alpha^{\pix{k}}}}}{\Prob*{\mat{u_\alpha^{\pix{k}}} \given \mat{Z_\alpha^{\pix{k}}}}}
\end{align}
\end{frame}
\begin{frame}[label=predictive_posterior]{Predictive Posterior}
\begin{align}
\Variat*{\mat{f_\ast} \given \mat{x_\ast}}
&= \int \sum_{k=1}^K \Variat*{a_\ast^{\pix{k}} \given \mat{x_\ast}} \Variat*{\mat{f_\ast^{\pix{k}}} \given \mat{x_\ast}} \diff \mat{a_\ast^{\pix{k}}} \\
&\approx \sum_{k=1}^K \hat{a}_\ast^{\pix{k}} \mat{\hat{f}_\ast^{\pix{k}}}
\end{align}
\end{frame}
\end{document}