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MBulli
2018-03-12 22:21:39 +01:00
parent c224967b19
commit 316b1d2911
11 changed files with 76 additions and 72 deletions
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tex/chapters/relatedwork.tex
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@@ -33,12 +33,12 @@ The term fast Gauss transform was coined by Greengard \cite{greengard1991fast} w
% However, the complexity grows exponentially with dimension. \cite{Improved Fast Gauss Transform and Efficient Kernel Density Estimation}
% FastKDE, passed on ECF and nuFFT
Recent methods based on the self-consistent KDE proposed by Bernacchia and Pigolotti \cite{bernacchia2011self} allow to obtain an estimate without any assumptions, i.e. the kernel and bandwidth are both derived during the estimation.
Recent methods based on the self-consistent KDE proposed by Bernacchia and Pigolotti \cite{bernacchia2011self} allow to obtain an estimate without any assumptions, \ie{} the kernel and bandwidth are both derived during the estimation.
They define a Fourier-based filter on the empirical characteristic function of a given dataset.
The computation time was further reduced by \etal{O'Brien} using a non-uniform fast Fourier transform (FFT) algorithm to efficiently transform the data into Fourier space \cite{oBrien2016fast}.
% binning => FFT
In general, it is desirable to omit a grid, as the data points do not necessarily fall onto equally spaced points.
In general, it is desirable to compute the estimate directly from the sample set.
However, reducing the sample size by distributing the data on an equidistant grid can significantly reduce the computation time, if an approximative KDE is acceptable.
Silverman \cite{silverman1982algorithm} originally suggested to combine adjacent data points into data bins, which results in a discrete convolution structure of the KDE.
Allowing to efficiently compute the estimate using a FFT algorithm.