# FKSUM v0.1.4

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## Fast Kernel Sums

Implements the method of Hofmeyr, D.P. (2019) <DOI:10.1109/TPAMI.2019.2930501> for fast evaluation of univariate kernel smoothers based on recursive computations. Applications to the basic problems of density and regression function estimation are provided, as well as some projection pursuit methods for which the objective is based on non-parametric functionals of the projected density, or conditional density of a response given projected covariates.

## Functions in FKSUM

 Name Description f_ica Projection index for independent component analysis. kndksum Kernel and kernel derivative sums FKSUM-package Fast Exact Kernel Smoothing fk_mdh Minimum density hyperplanes ksum Kernel sums fk_md_dp C++ code for evaluating partial gradient of mimimum density hyperplane w.r.t. projected data plot.fk_ppr Plot method for class fk_ppr bin_wts Compute discrete bin weights fk_md_b Minimum density hyperplane orthogonal to a vector fk_md C++ code for evaluating mimimum density hyperplane from projected data plot.fk_mdh Plot method for class fk_mdh df_ppr Gradient of the projection index for projection pursuit regression fk_sum Fast Exact Kernel Sum Evaluation h_Gauss_to_K Bandwidth conversion from Gaussian print.fk_mdh Print method for class fk_mdh cbin_alloc Allocation of points to bins predict.fk_regression Predict method for class fk_regression fk_density Fast univariate kernel density estimation df_ica Gradient of projection index for independent component analysis. dksum Kernel derivative sums h_K_to_Gauss Bandwidth conversion to Gaussian fk_NW Nadaraya-Watson regression estimator fk_fmdh Projection index for finding minimum density hyperplanes fk_dfmdh Gradient of projection index for finding minimum density hyperplanes fancy_PPR_initialisation Initialisation for PPR based on Ridge LM after GAM type smoothing fk_is_minim_md Check if MDH constraints are active predict.fk_ppr Predict method for class fk_ppr whiten Whitening (standardising) a data matrix print.fk_ppr Print method for class fk_ppr fk_ICA Independent component analysis with sample entropy estimated via kernel density plot.fk_regression Plot method for class fk_regression kLLreg Leave-one-out regression smoother sm_bin_wts Compute smoothed bin weights fk_ppr Projection pursuit regression with local linear kernel smoother plot.fk_ICA Plot method for class fk_ICA fk_loc_lin Local linear regression estimator norm_K The L2 norm of a kernel plot.fk_density Plot method for class fk_density print.fk_ICA Print method for class fk_ICA fk_regression Fast univariate kernel regression norm_const_K Normalising constant for kernels in FKSUM var_K Variance of a kernel plot_kernel Plot the shape of a kernel function implemented in FKSUM based on its vector of beta coefficients print.fk_density Print method for class fk_density print.fk_regression Print method for class fk_regression roughness_K Kernel roughness f_ppr Projection index for projection pursuit regression No Results!