\begin{table}[ht]
  \caption{List of frequently used symbols.}
  \label{tab-notation}
  \centering
  \begin{tabular}{|c|l|}
  \hline
  \textbf{Symbol} & \textbf{Description} \\
  \hline\hline
  $\mathcal{D}$, $\bm{x}$ & Data set in $\mathbb{R}^m$ and data point in $\mathcal{D}$ \\
  $n$, $m$ & Size and dimensionality of $\mathcal{D}$ \\
  $d(\cdot, \cdot)$ & (Metric) distance function \\
  $\mathcal{H}$, $h(\cdot)$ & LSH scheme for $d(\cdot, \cdot)$ and LSH function drawn from $\mathcal{H}$ \\
  $\omega$ & Bandwidth parameter in ($l_2$-LSH function) $h(\cdot)$ \\
  $k(\cdot, \cdot)$ & LSH kernel function defined on $\mathcal{H}$ \\
  $\mathrm{KDE}_{\mathcal{D}}(\bm{q})$ & Kernel density of $\mathcal{D}$ at query point $\bm{q}$ \\
  $\widehat{\mathrm{KDE}}_{\mathcal{D}}(\bm{q})$ & Approximation of $\mathrm{KDE}_{\mathcal{D}}(\bm{q})$ \\
  $\varepsilon$ & Privacy budget \\
  $d_{\chi}(\cdot, \cdot)$ & Metric distance function for mLDP derived from $d(\cdot, \cdot)$ \\
  $\alpha$ & Error parameter in approximation bound \\
  $\eta$ & Confidence parameter in approximation and privacy bounds \\
  $\mathcal{S}_{\mathcal{D}}$ & Sketch built on $\mathcal{D}$ for KDE queries \\
  $L$, $R$ & Number \& range of LSH functions (height \& width of $\mathcal{S}_{\mathcal{D}}$) \\
  $H, \widehat{H}$ & Sequences of hash values before and after perturbation \\
  \hline
  \end{tabular}
\end{table}
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