source_extract/main.tex

%%%%%%%% ICML 2026 EXAMPLE LATEX SUBMISSION FILE %%%%%%%%%%%%%%%%%

\documentclass{article}

% Recommended, but optional, packages for figures and better typesetting:
\usepackage{microtype}
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\usepackage{subcaption}
\usepackage{booktabs} % for professional tables
\usepackage{multirow}
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% Attempt to make hyperref and algorithmic work together better:
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% Use the following line for the initial blind version submitted for review:
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% For preprint, use
% \usepackage[preprint]{icml2026}

% If accepted, instead use the following line for the camera-ready submission:
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\usepackage{amsthm}
\usepackage{enumitem}

\usepackage{tikz}
% \usetikzlibrary{positioning, trees, arrows.meta, shadows, backgrounds}
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\usepackage{amsmath, amssymb}
\usepackage{caption}
\usepackage{makecell}
\usepackage{arydshln}


% if you use cleveref..
\usepackage[capitalize,noabbrev]{cleveref}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% THEOREMS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{assumption}[theorem]{Assumption}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{example}{Example}[section]
% Todonotes is useful during development; simply uncomment the next line
%    and comment out the line below the next line to turn off comments
%\usepackage[disable,textsize=tiny]{todonotes}
\usepackage[textsize=tiny]{todonotes}

% \raggedbottom

% The \icmltitle you define below is probably too long as a header.
% Therefore, a short form for the running title is supplied here:
\icmltitlerunning{Tree-Structured Orthonormal Decomposition of the Aitchison Simplex}

\begin{document}

\twocolumn[
  \icmltitle{Tree-Structured Orthonormal Decomposition of the Aitchison Simplex}

  % It is OKAY to include author information, even for blind submissions: the
  % style file will automatically remove it for you unless you've provided
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  % List of affiliations: The first argument should be a (short) identifier you
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  % affiliations should list Company, City, Region, Country

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  \begin{icmlauthorlist}
    \icmlauthor{Daisuke Yamada}{yyy}
    \icmlauthor{Qijun Zhang}{yyy}
    \icmlauthor{Travis Pence}{yyy}
    \icmlauthor{Barbara B. Bendlin}{yyy}
    \icmlauthor{Federico Rey}{yyy}
    \icmlauthor{Vikas Singh}{yyy}
    % \icmlauthor{Firstname4 Lastname4}{sch}
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    %\icmlauthor{}{sch}
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  \icmlaffiliation{yyy}{University of Wisconsin Madison, Madison WI, USA}
  % \icmlaffiliation{comp}{Company Name, Location, Country}
  % \icmlaffiliation{sch}{School of ZZZ, Institute of WWW, Location, Country}

  \icmlcorrespondingauthor{Daisuke Yamada}{dyamada2@wisc.edu}
  % \icmlcorrespondingauthor{Firstname2 Lastname2}{first2.last2@www.uk}

  % You may provide any keywords that you find helpful for describing your
  % paper; these are used to populate the "keywords" metadata in the PDF but
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  \icmlkeywords{Machine Learning, ICML}

  \vskip 0.3in
]

% this must go after the closing bracket ] following \twocolumn[ ...

% This command actually creates the footnote in the first column listing the
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% command is standard text for equal contribution. Remove it (just {}) if you
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% Use ONE of the following lines. DO NOT remove the command.
% If you have no special notice, KEEP empty braces:
\printAffiliationsAndNotice{}  % no special notice (required even if empty)
% Or, if applicable, use the standard equal contribution text:
% \printAffiliationsAndNotice{\icmlEqualContribution}

%%%%%%% MAIN  %%%%%%%%%%

% \input{section/outline}
\input{section-camera/abstract}
\input{section-camera/introduction}
\input{section-camera/background}
\input{section-camera/problem}
\input{section-camera/method}
\input{section-camera/interpret}
\input{section-camera/experiment}
\input{section-camera/beyond_comp}
\input{section-camera/related_work}
\input{section-camera/conclusion}

\newpage

{\color{black}
\section*{Acknowledgments}
We thank the anonymous reviewers for their constructive feedback. We are grateful to Prof.~Colin Dewey and Prof. Christina Kendziorski for discussions and feedback. Authors were all partly supported by NIH R01AG092220.
}

\section*{Impact Statement}
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.



\bibliographystyle{icml2026}
\bibliography{reference}

% In the unusual situation where you want a paper to appear in the
% references without citing it in the main text, use \nocite
% \nocite{langley00}

%%%%%% APPENDIX %%%%%%%%
\newpage
\appendix
\onecolumn

% \input{section-camera/appendix/limitations}
\input{section-camera/appendix/proofs_algo}
\input{section-camera/appendix/additional_exp}


\end{document}