\documentclass[accepted]{uai2024}

\usepackage[american]{babel}

\usepackage{natbib}
\bibliographystyle{plainnat}
\renewcommand{\bibsection}{\subsubsection*{References}}

\usepackage{mathtools}
\usepackage{booktabs}
\usepackage{tikz}
\usepackage{graphicx}
\usepackage{amsmath, amssymb, amsfonts, amsthm}
\usepackage{enumitem}
\usepackage{bm}
\usepackage{color}
\usepackage{url}
\usepackage{booktabs}
\usepackage{threeparttable}
\usepackage{multirow}
\usepackage[ruled,vlined]{algorithm2e}
\usepackage{algpseudocode}
\usepackage{array}
\usepackage[]{mdframed}

\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\SetKwComment{Comment}{$\triangleright$\ }{}

\renewcommand{\paragraph}[1]{\noindent\textbf{#1.}}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}

\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}
\newtheorem{proposition}{Proposition}

\title{Approximate Kernel Density Estimation under\\Metric-based Local Differential Privacy}

\author[1]{Yi~Zhou}
\author[1]{\href{mailto:yhwang@dase.ecnu.edu.cn}{Yanhao~Wang\thanks{Corresponding author.}}{}}
\author[1]{Long~Teng}
\author[2]{Qiang~Huang}
\author[1]{Cen~Chen}
\affil[1]{%
    School of Data Science and Engineering\\
    East China Normal University\\
    Shanghai, China
}
\affil[2]{%
    School of Computing\\
    National University of Singapore\\
    Singapore
}

\begin{document}
  
\maketitle

\input{sections/0-abstract}
\input{sections/1-introduction}
\input{sections/2-literature}
\input{sections/3-definition}
\input{sections/4-algorithms}
\input{sections/5-analysis}
\input{sections/6-experiments}
\input{sections/7-conclusion}

\begin{acknowledgements}
We thank anonymous reviewers for their constructive comments to help improve this paper.
This research was supported by the National Natural Science Foundation of China under Grant Numbers 62202169 and 62202170, the Open Research Fund of KLATASDS-MOE, ECNU, and the Ministry of Education, Singapore, under its MOE AcRF TIER 3 Grant (MOE-MOET32022-0001).
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the Ministry of Education, Singapore.
\end{acknowledgements}

\bibliography{references}

\input{sections/appendix}

\end{document}
