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toni
2018-02-15 23:40:41 +01:00
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@@ -105,8 +105,9 @@ A naive implementation of \eqref{eq:binKde} reduces the number evaluations to $\
Due to the fixed grid spacing a faster $\landau{G}$ algorithm can be used, because most of the kernel evaluations are the same and can be reused.
%, as each $g_j-g_{j-k}=k\delta$ is independent of $j$ \cite{fan1994fast}.
This is usually highlighted as the striking computational benefit of the BKDE.
\commentByToni{Das liest sich jetzt so, als wäre der BKDE schon sau schnell. Warum machen wir dann überhaupt noch was?}
However, for this work it is key to recognize the discrete convolution structure of \eqref{eq:binKde}, as this allows one to interpret the computation of a density estimate as a signal filter problem.
However, for this work it is the key to recognize the discrete convolution structure of \eqref{eq:binKde}, as this allows one to interpret the computation of a density estimate as a signal filter problem.
This makes it possible to apply a wide range of well studied techniques from the broad field of digital signal processing (DSP).
Using the Gaussian kernel from \eqref{eq:gausKern} in conjunction with \eqref{eq:binKde} results in the following equation
\begin{equation}