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\title{Accurate and Scalable Stochastic Gaussian Process Regression \\
via Learnable Coreset-based Variational Inference}

% 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]{\href{mailto:<mk4139@columbia.edu>?Subject=Your CVGP work on UAI 2025}{Mert Ketenci}{}}
\author[2]{{Adler Perotte}}
\author[1,2]{Noémie Elhadad}
\author[3,4]{\href{mailto:<iurteaga@bcamath.org>?Subject=Your CVGP work on UAI 2025}{I\~{n}igo Urteaga}}
% Add affiliations after the authors
\affil[1]{%
    Department of Computer Science\\
    Columbia University \\
    New York, USA
}
\affil[2]{%
    Department of Biomedical Informatics\\
    Columbia University \\
    New York, USA
}
\affil[3]{%
BCAM --- Basque Center for Applied Mathematics\\
Bilbao, Spain
}
\affil[4]{%
IKERBASQUE --- Basque Foundation for Science\\
Bilbao, Spain
}
  
  \begin{document}

\maketitle

\begin{abstract}
We introduce a novel stochastic variational inference method for Gaussian process ($\gp$) regression, by deriving a $\gp$ posterior over a learnable set of coresets:
\ie over pseudo-input/output, weighted pairs.
Unlike former free-form variational families for stochastic inference,
our coreset-based variational $\gp$ (CVGP)\footnote{Code is publicly available at \href{https://github.com/iurteagalab/cvgp_regression}{https://github.com/iurteagalab/cvgp\_regression}.}
is defined in terms of the $\gp$ prior and the (weighted) data likelihood.
This formulation naturally incorporates inductive biases of the prior,
and ensures its kernel and likelihood dependencies are shared with the posterior.
We derive a variational lower-bound on the log-marginal likelihood by marginalizing over the latent $\gp$ coreset variables,
and show that CVGP's lower-bound is amenable to stochastic optimization.
CVGP reduces the dimensionality of the variational parameter search space to linear $\bigO{M}$ complexity, while ensuring numerical stability at $\bigO{M^3}$ time complexity and $\bigO{M^2}$ space complexity.
Evaluations on real-world and simulated regression problems demonstrate that CVGP achieves superior inference and predictive performance
than state-of-the-art, stochastic sparse $\gp$ approximation methods.
\end{abstract}

% Introduction
\section{Introduction}

\label{sec:introduction}
\input{tex_sections/intro}

% Background
\section{Background}

\label{sec:background}
\input{./tex_sections/background}

% CVGP
\section{Coreset-based Variational Posterior $\gp$ (CVGP)}

\label{sec:method}
\input{./tex_sections/method}

% Experiments
\section{Experiments}

\label{sec:experiments}
\input{./tex_sections/experiments}
% Conclusions

\section{Conclusion}

\label{sec:conclusions}
\input{./tex_sections/conclusions}

% \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
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 %    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,

Mert Ketenci acknowledges this research is supported
by NHLBI award R01HL148248.
I\~{n}igo Urteaga acknowledges the support of “la Caixa” foundation’s LCF/BQ/PI22/11910028 award,
as well as funds by MICIU/AEI/10.13039/501100011033 and the BERC 2022-2025 program funded by the Basque Government.

\end{acknowledgements}

% Refernces
\bibliography{main}

\newpage
\onecolumn

\title{Supplementary Material: Accurate and Scalable Stochastic Gaussian Process Regression via Learnable Coreset-based Variational Inference}
\maketitle
\appendix
\input{./supplement}

\end{document}
