Intro & related work

tex/chapters/experiments.tex

@@ -1,2 +1,27 @@
 \section{Experiments}
+We now empirically evaluate the accuracy of our method and compare its runtime performance with other state of the art approaches.
+To conclude our findings we present a real world example from a indoor localisation system.
 
+All tests are performed on a Intel Core \mbox{i5-7600K} CPU with a frequency of $4.5 \text{GHz}$, which supports the AVX2 instruction set, hence 256-bit wide SIMD registers are available.
+We compare our C++ implementation of the box filter based KDE to the KernSmooth R package and the \qq{FastKDE} implementation \cite{fastKDE}.
+The KernSmooth packages provides a FFT-based BKDE implementation based on optimized C functions at its core.
+
+\subsection{Error}
+In order to quantity the accuracy of our method the mean integrated squared error (MISE) is used.
+The ground truth is given as a synthetic data set drawn from a mixture normal density.
+Clearly, the choice of the ground truth distribution affects the resulting error.
+However, as our method approximates the KDE it is only of interest to evaluate the closeness to the KDE and not to the ground truth itself.
+Therefore, the particular choice of the ground truth is only of minor importance here.
+
+At first we evaluate the accuracy of our method as a function of the bandwidth $h$ in comparison to the exact KDE and the BKDE.
+
+
+
+% kde, box filter, exbox in abhänigkeit von h (bild)
+% sample size und grid size text
+% fastKDE fehler vergleich macht kein sinn weil kernel und bandbreite unterschiedlich sind
+
+
+\subsection{Performance}
+
+\subsection{Real World}