KernelDensityEstimation Struct Reference

Kernel Density Estimation utilities using FFT-based methods. More...

#include <OpenMS/MATH/STATISTICS/KernelDensityEstimation.h>

Static Public Member Functions
static double	bwNrd0 (const std::vector< double > &x)
	Bandwidth selector using the "nrd0" rule-of-thumb for kernel density estimation.
static std::vector< double >	linBin (const std::vector< double > &x, double xmin, double xmax, std::size_t nbins, const std::vector< double > *weights)
	Linear binning of data onto an equally-spaced grid.
static std::vector< double >	linBin (const std::vector< double > &x, double xmin, double xmax, std::size_t nbins)
	Convenience overload that uses uniform weights.
static std::vector< double >	forRt (const std::vector< double > &X, std::size_t M=0)
	Forward FFT of real-valued data using Munro-packed format.
static std::vector< double >	revRt (const std::vector< double > &Xp, std::size_t M=0)
	Inverse FFT of Munro-packed data to real-valued output.
static std::vector< double >	silvermanKernelFFT (double bw, std::size_t M, double RANGE)
	Compute the FFT of a Gaussian kernel in Munro-packed format.
static std::pair< std::vector< double >, std::vector< double > >	gridKdeFFT (const std::vector< double > &x, double bw, std::size_t gridsize=512, double cut=3.0)
	Fast kernel density estimation on a regular grid using FFT convolution.
static std::vector< double >	kdeFFTEval (const std::vector< double > &x, double bw, std::size_t gridsize=512, double cut=3.0)
	Evaluate kernel density estimates at the data points themselves.

Detailed Description

Kernel Density Estimation utilities using FFT-based methods.

This class provides efficient kernel density estimation using Fast Fourier Transform (FFT) based convolution, following the Silverman (1982) algorithm as implemented in Python's statsmodels package.

The FFT-based approach scales as O(n + M*log(M)) compared to O(n*M) for direct evaluation, making it highly efficient for large datasets or fine grids.

Key features:

• Automatic bandwidth selection using Silverman's rule-of-thumb
• FFT-based convolution for fast computation
• Linear binning for grid-based estimation
• Munro-packed real FFT for memory efficiency

References: Silverman BW. (1982) "Algorithm AS 176: Kernel density estimation using the Fast Fourier Transform." J. R. Statist. Soc. C 31(1):93-99. DOI: 10.2307/2347084

Member Function Documentation

linBin()

static std::vector< double > linBin ( const std::vector< double > &  x, double  xmin, double  xmax, std::size_t  nbins  )

static

Convenience overload that uses uniform weights.