\documentclass[accepted]{uai2024} % for initial submission
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% colors
% \definecolor{yellow}{RGB}{255,255,191}
\definecolor{lightgreen}{RGB}{178,223,138}  % RBF
\definecolor{darkgreen}{RGB}{51,160,44}     % Laplace
\definecolor{gold}{RGB}{255,215,0}          % deep kernel learning
\definecolor{lightblue}{RGB}{171,217,233}   % ARD-RBF
\definecolor{darkblue}{RGB}{44,123,182}     % ARD-Laplace
\definecolor{purple}{RGB}{138,43,226}       % ARD-Laplace-full
\definecolor{blackgray}{RGB}{130,130,130}   % RFM-Laplace
\definecolor{lightgray}{RGB}{180,180,180}   % RFM-Laplace-diag
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\title{Uncertainty Estimation with Recursive Feature Machines}


% Add authors
\author[1]{\href{mailto:daniel.gedon@it.uu.se?Subject=Your UAI 2024 paper}{\textcolor{black}{Daniel~Gedon}}\thanks{Equal contribution.}}
\author[2]{Amirhesam~Abedsoltan\protect\footnotemark[1]}
\author[1]{Thomas~B.~Schön}
\author[2,3]{Mikhail~Belkin}
% Add affiliations after the authors
\affil[1]{%
    Department of Information Technology\\
    Uppsala University\\
    Sweden
}
\affil[2]{%
    Department of Computer Science and Engineering\\
    UC San Diego\\
    USA
}
\affil[3]{%
    Halıcıoğlu Data Science Institute\\
    UC San Diego\\
    USA
}




  
\begin{document}
\maketitle
\addtocontents{toc}{\protect\setcounter{tocdepth}{0}} % do not add to list of tables for appendix.



\begin{abstract}
    In conventional regression analysis, predictions are typically represented as point estimates derived from covariates. The Gaussian Process (GP) offer a kernel-based framework that predicts and quantifies associated uncertainties. However, kernel-based methods often underperform ensemble-based decision tree approaches in regression tasks involving tabular and categorical data. Recently, Recursive Feature Machines (RFMs) were proposed as a novel feature-learning kernel which strengthens the capabilities of kernel machines. In this study, we harness the power of these RFMs in a probabilistic GP-based approach to enhance uncertainty estimation through feature extraction within kernel methods. We employ this learned kernel for in-depth uncertainty analysis. On tabular datasets, our RFM-based method surpasses other leading uncertainty estimation techniques, including NGBoost and CatBoost-ensemble. Additionally, when assessing out-of-distribution performance, we found that boosting-based methods are surpassed by our RFM-based approach.%\looseness=-1
\end{abstract}








\input{sections/introduction}
\input{sections/priorwork}
\input{sections/method}
\input{sections/experiments}
\input{sections/discussion}










% \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
%                       % 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
                         % Briefly acknowledge people and organizations here.
    This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. % DG
    The computations were enabled by the Berzelius resource provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre, Sweden. % DG

    A.A and M.B are grateful for the support from the National Science Foundation (NSF) and the Simons Foundation for the Collaboration on the Theoretical Foundations of Deep Learning (\url{https://deepfoundations.ai/}) through awards DMS-2031883 and \#814639  and the TILOS institute (NSF CCF-2112665).
\end{acknowledgements}





% References
\bibliography{references}







\newpage

\onecolumn

\title{Uncertainty Estimation with Recursive Feature Machines\\(Supplementary Material)}
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\maketitle


\appendix
\input{sections/appendix}








\end{document}
