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

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    \icmlauthor{Qijun Zhang}{yyy}
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    \icmlauthor{Federico Rey}{yyy}
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{\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.



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%%%%%% APPENDIX %%%%%%%%
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\appendix
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