# FKSUM v0.1.0

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## Fast Kernel Sums

Implements the method of Hofmeyr, D.P. (2019) <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 cbin_alloc Allocation of points to bins fk_ICA Independent component analysis with sample entropy estimated via kernel density f_ppr Projection index for projection pursuit regression df_ppr Gradient of the projection index for projection pursuit regression dksum Kernel derivative sums FKSUM-package Fast Exact Kernel Smoothing f_ica Projection index for independent component analysis. fancy_PPR_initialisation Initialisation for PPR based on Ridge LM after GAM type smoothing df_ica Gradient of projection index for independent component analysis. bin_wts Compute discrete bin weights fk_md_dp C++ code for evaluating partial gradient of mimimum density hyperplane w.r.t. projected data fk_md_b Minimum density hyperplane orthogonal to a vector fk_md C++ code for evaluating mimimum density hyperplane from projected data fk_mdh Minimum density hyperplanes fk_fmdh Projection index for finding minimum density hyperplanes fk_dfmdh Gradient of projection index for finding minimum density hyperplanes fk_NW Nadaraya-Watson regression estimator fk_density Fast univariate kernel density estimation fk_loc_lin Local linear regression estimator fk_is_minim_md Check if MDH constraints are active kndksum Kernel and kernel derivative sums fk_sum Fast Exact Kernel Sum Evaluation norm_const_K Normalising constant for kernels in FKSUM h_K_to_Gauss Bandwidth conversion to Gaussian norm_K The L2 norm of a kernel fk_ppr Projection pursuit regression with local linear kernel smoother kLLreg Leave-one-out regression smoother fk_regression Fast univariate kernel regression h_Gauss_to_K Bandwidth conversion from Gaussian whiten Whitening (standardising) a data matrix var_K Variance of a kernel ksum Kernel sums roughness_K Kernel roughness sm_bin_wts Compute smoothed bin weights plot_kernel Plot the shape of a kernel function implemented in FKSUM based on its vector of beta coefficients predict.fk_ppr Predict method for class fk_ppr No Results!