\documentclass[accepted]{uai2025} % for initial submission
%\documentclass[accepted]{uai2025} % after acceptance, for a revised version; 
% also before submission to see how the non-anonymous paper would look like 
                        
%% There is a class option to choose the math font
% \documentclass[mathfont=ptmx]{uai2025} % ptmx math instead of Computer
                                         % Modern (has noticeable issues)
% \documentclass[mathfont=newtx]{uai2025} % newtx fonts (improves upon
                                          % ptmx; less tested, no support)
% NOTE: Only keep *one* line above as appropriate, as it will be replaced
%       automatically for papers to be published. Do not make any other
%       change above this note for an accepted version.

%% Choose your variant of English; be consistent
\usepackage[american]{babel}
% \usepackage[british]{babel}

%% Some suggested packages, as needed:
\usepackage{natbib} % has a nice set of citation styles and commands
    \bibliographystyle{plainnat}
    \renewcommand{\bibsection}{\subsubsection*{References}}
\usepackage{mathtools} % amsmath with fixes and additions
% \usepackage{siunitx} % for proper typesetting of numbers and units
\usepackage{booktabs} % commands to create good-looking tables
\usepackage{tikz} % nice language for creating drawings and diagrams


\usepackage{graphicx}
\usepackage{amsfonts,enumitem,amsmath,amsthm}
\renewcommand{\proof}{\textit{Proof. }}
\usepackage{microtype}      % microtypography
\usepackage{xcolor}         % colors
\usepackage{float}          % float
\usepackage{subfigure}      % subfigures
\usepackage{multirow}

\usepackage{graphicx,appendix,amssymb}
\usepackage[normalem]{ulem}
\usepackage{soul}
\usepackage{makecell}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{corollary}{Corollary}
\newtheorem{remark}{Remark}

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%           redefining \footnotesize, we provide the original \footnotesize
%           using this macro.
%           (Use only sparingly, e.g., in drawings, as it is quite small.)

%% Self-defined macros
\newcommand{\swap}[3][-]{#3#1#2} % just an example

\newcommand{\ao}[1]{\textcolor[rgb]{0,0,1}{[azim: #1]}} 

\title{Do Vendi Scores Converge with Finite Samples?\\
Truncated~Vendi Score for Finite-Sample Convergence Guarantees %On the Statistical Complexity of Estimating Vendi Scores from Empirical 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]{\href{mailto:<aospanov9@cse.cuhk.edu.hk>?Subject=Your UAI 2025 paper}{Azim Ospanov}{}}
\author[1]{\href{mailto:<farnia@cse.cuhk.edu.hk>?Subject=Your UAI 2025 paper}{Farzan Farnia}{}}
% Add affiliations after the authors
\affil[1]{%
    Department of Computer Science and Engineering, 
    The Chinese University of Hong Kong}
    
\begin{document}
\maketitle

\begin{abstract}
    \input{paper-text/1-abstract}
\end{abstract}

\section{Introduction}
\input{paper-text/2-introduction}

\vspace{-3mm}
\section{Related Works}
\input{paper-text/3-related-works}

\vspace{-3mm}
\section{Preliminaries}
\input{paper-text/4-preliminaries}

\vspace{-3mm}
\section{Statistical Convergence of Vendi and RKE Scores}% with Finite and Infinite Kernel Maps}
\input{paper-text/5-statistical_convergence}

\vspace{-3mm}
\section{Truncated Vendi Score and its Estimation via Proxy Kernels}
%\section{Truncated population Vendi and its Estimation via Proxy Kernels}
\input{paper-text/5b-proxymethod-analysis}

\vspace{-3mm}
\section{Numerical Results}
\input{paper-text/6-numerical-results}


\section{Conclusion}

\input{paper-text/7-conclusion}

\begin{acknowledgements} 
This work is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by CUHK Direct Research Grants with CUHK Project No. 4055164 and 4937054.
Finally, the authors thank the anonymous reviewers for their thoughtful feedback and constructive suggestions.

\end{acknowledgements}

\clearpage
\clearpage



% References
\bibliography{references}

\newpage

\onecolumn
\input{paper-text/10-appendix}



\end{document}
