From 40be309b50b61f68e3bf9347db0e3dd318eae6de Mon Sep 17 00:00:00 2001 From: toni Date: Thu, 15 Feb 2018 23:40:41 +0100 Subject: [PATCH] added a comment --- tex/chapters/kde.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/tex/chapters/kde.tex b/tex/chapters/kde.tex index 199767b..acbbd2e 100644 --- a/tex/chapters/kde.tex +++ b/tex/chapters/kde.tex @@ -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}