%\documentclass{uai2025} % for initial submission
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\subsubsection*{References}}
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\title{Nonlinear Causal Discovery for Grouped Data}

% The standard author block has changed for UAI 2025 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
%
% Add authors
\author[1,4]{\href{mailto:<konstantin.goebler@tum.de>?Subject=Your UAI 2025 paper}{Konstantin~Göbler}{}}
\author[3]{Tobias~Windisch}
\author[1,2]{Mathias~Drton}

\affil[1]{%
  Department of Mathematics\\
  TUM School of Computation, Information and Technology\\
  Technical University of Munich
}
\affil[2]{%
  Munich Center for Machine Learning
}
\affil[3]{%
  University of Applied Sciences Kempten\\
  Faculty of Mechanical Engineering
}
\affil[4]{%
  Robert Bosch GmbH
}

\begin{document}
\maketitle

\begin{abstract}
  \input{Sections/abstract.tex}
\end{abstract}

\section{Introduction}\label{sec:introduction}
\input{Sections/introduction.tex}

\section{Methodology}\label{sec:methodology}
\input{Sections/prerequisites.tex}
\subsection{Causal models for grouped data}\label{sec:causal_models}
\input{Sections/identifiability.tex}

\section{Grouped RESIT}\label{sec:groupresit}
\input{Sections/resit.tex}
\input{Sections/murgs.tex}
\section{Experiments}\label{sec:experiments}
\input{Sections/experiments.tex}
\section{Real manufacturing data application}\label{sec:real_data}
\input{Sections/real_data_analysis.tex}

\section{Conclusions}\label{sec:conclusions}

\input{Sections/conclusions.tex}

% \begin{contributions} % will be removed in pdf for initial submission
%   % (without ‘accepted’ option in \documentclass)
%   % so you can already fill it to test with the
%   % ‘accepted’ class option
%   Briefly list author contributions.
%   This is a nice way of making clear who did what and to give proper credit.
%   This section is optional.

%   H.~Q.~Bovik conceived the idea and wrote the paper.
%   Coauthor One created the code.
%   Coauthor Two created the figures.
% \end{contributions}

\begin{acknowledgements} % will be removed in pdf for initial submission,
  % (without ‘accepted’ option in \documentclass)
  % so you can already fill it to test with the
  % ‘accepted’ class option
  The authors gratefully acknowledge Andrew McCormack, Martin Roth, and Hongjian Shi for their insightful discussions and valuable feedback. We also thank the anonymous referees whose thoughtful suggestions greatly improved the clarity and quality of this work. Mathias Drton acknowledges funding from the German Federal Ministry of Education and Research and the Bavarian State Ministry for Science and the Arts.
\end{acknowledgements}

% References
\bibliography{main}

\newpage

\title{Nonlinear Causal Discovery for Grouped Data\\(Supplementary Material)}
\maketitle

\appendix

\section{Proofs of Identifiability}\label{sec:proofs_A}
\input{Sections/identifiability_proofs.tex}

\section{Proof of Backfitting Update}\label{sec:backfitting_update}

\input{Sections/appendix_a.tex}

\section{Simulation Details}\label{sec:simulation_details}

\input{Sections/simulation_details.tex}

\section{Additional Results}\label{sec:additional_results}
\input{Sections/additional_results.tex}

\end{document}
