Title: Fast Local Polynomial Regression and Kernel Density Estimation
Version: 1.0.1
Description: Non-Uniform Fast Fourier Transform ('NUFFT')-accelerated local polynomial regression and kernel density estimation for large, scattered, or complex-valued datasets. Provides automatic bandwidth selection via Generalized Cross-Validation (GCV) for regression and Likelihood Cross-Validation (LCV) for density estimation. This is the 'R' port of the 'fastLPR' 'MATLAB'/'Python' toolbox, achieving O(N + M log M) computational complexity through custom 'NUFFT' implementation with Gaussian gridding. Supports 1D/2D/3D data, complex-valued responses, heteroscedastic variance estimation, and confidence interval computation. Performance optimized with vectorized 'R' code and compiled helpers via 'Rcpp'/'RcppArmadillo'. Extends the 'FKreg' toolbox of Wang et al. (2022) <doi:10.48550/arXiv.2204.07716> with 'Python' and 'R' ports. Applied in Li et al. (2022) <doi:10.1016/j.neuroimage.2022.119190>. Uses 'NUFFT' methods based on Greengard and Lee (2004) <doi:10.1137/S003614450343200X>, binning-accelerated kernel estimation of Wand (1994) <doi:10.1080/10618600.1994.10474656>, and local polynomial regression framework of Fan and Gijbels (1996, ISBN:978-0412983214).
License: GPL-3
Encoding: UTF-8
ByteCompile: false
Depends: R (≥ 4.2.0)
Imports: stats, utils, grDevices, graphics, compiler, Rcpp (≥ 1.0.0)
Suggests: testthat (≥ 3.0.0), akima, rgl, R.matlab
LinkingTo: Rcpp, RcppArmadillo
SystemRequirements: GNU make
URL: https://github.com/rigelfalcon/fastLPR
BugReports: https://github.com/rigelfalcon/fastLPR/issues
RoxygenNote: 7.3.1
NeedsCompilation: yes
Packaged: 2026-04-14 01:51:00 UTC; PC
Author: Ying Wang [aut, cre], Min Li [aut]
Maintainer: Ying Wang <yingwangrigel@gmail.com>
Repository: CRAN
Date/Publication: 2026-04-21 08:20:02 UTC

Fast Kernel Density Estimation with automatic bandwidth selection

Description

Performs kernel density estimation using NUFFT acceleration with automatic bandwidth selection via Likelihood Cross-Validation (LCV).

Usage

cv_fastkde(x, h = NULL, opt = NULL)

Arguments

x

N x d matrix of data points (N samples, d dimensions).

h

Bandwidth parameter(s) or grid for LCV selection.

opt

Options list with fields similar to cv_fastlpr.

Value

KDE results list containing estimated density, evaluation grid, and LCV results.

See Also

cv_fastlpr, get_hlist

Examples


x <- matrix(rnorm(200), ncol = 1)
kde <- cv_fastkde(x)

Fast Local Polynomial Regression with automatic bandwidth selection

Description

This is the main function for fastLPR toolbox. It performs nonparametric regression using kernel-weighted local polynomial methods with NUFFT (Non-Uniform Fast Fourier Transform) acceleration. The function automatically selects the optimal bandwidth via Generalized Cross-Validation (GCV) when multiple bandwidth candidates are provided.

Usage

cv_fastlpr(x, y, h = NULL, opt = NULL)

Arguments

x

N x d matrix of predictors (N samples, d dimensions). Can be real or complex-valued. Each row is one observation. For complex-valued predictors, use x = real + 1i*imag.

y

N x 1 vector of responses. Can be real or complex-valued. Must have same number of rows as x.

h

Bandwidth parameter(s) (optional, default: automatic selection). Scalar: same bandwidth for all dimensions. 1 x d vector: different bandwidth per dimension. k x d matrix: grid of k bandwidth combinations for GCV selection. Use get_hlist() to generate bandwidth candidates.

opt

Options list (optional) with fields:

order

Polynomial order (default: 0) 0 = Nadaraya-Watson (local constant) 1 = Local linear regression 2 = Local quadratic regression

kernel_type

Kernel function (default: 'gaussian') 'gaussian' or 'epanechnikov'

dstd

Number of DOF samples for variance estimation (default: 0) Set to 5-20 for heteroscedastic variance estimation

y_type_out

Output type (default: 'mean') 'mean' = estimate conditional mean E[Y|X] 'variance' = estimate conditional variance Var[Y|X]

N

Grid resolution for evaluation (default: auto)

xrange

Evaluation range (default: data range)

seed

Random seed for Monte Carlo DOF estimation (default: NULL, no seed set). Set to an integer for reproducible bandwidth selection.

verbose

Logical. Print bandwidth selection details (default: FALSE).

Value

Regression results list containing:

yhat

Fitted values at evaluation grid points (N_grid x 1)

fpp_yhat

Interpolant object for prediction at any point. Use: y_pred = regs$fpp_yhat(x_new)

gcv_yhat

GCV results list (if multiple bandwidths provided)

h1se

Selected bandwidth (1-SE rule)

hmin

Bandwidth with minimum GCV

gcv

GCV values for all bandwidths

xq

Evaluation grid points (list for multi-dimensional)

xlist

Grid vectors (list)

opt

Options used for regression

xraw

Original predictor data

yraw

Original response data

Author(s)

Ying Wang, Min Li

References

Wang, Y., & Li, M. (2024). Fast and Exact Kernel-Weighted Regression for Large-Scale Scattered and Complex-Valued Data. Journal of Statistical Software (under review).

See Also

cv_fastkde, get_hlist, fastlpr_interval, fastlpr_plot

Examples


# Example 1: 1D regression with automatic bandwidth selection
x <- matrix(runif(500) * 20, ncol = 1)
y <- sin(x) + 0.2 * rnorm(500)
hlist <- get_hlist(20, c(0.01, 1), "logspace")
opt <- list(order = 1)  # Local linear
regs <- cv_fastlpr(x, y, hlist, opt)

# Plot results
plot(x, y, pch = ".", col = "black")
# Note: fpp_yhat is an interpolation function
x_pred <- seq(min(x), max(x), length.out = 100)
y_pred <- regs$fpp_yhat(x_pred)
lines(x_pred, y_pred, col = "blue", lwd = 2)

Plot KDE results

Description

Visualizes kernel density estimation results.

Usage

fastkde_plot(fpp, x_range = NULL, n_points = 1000, ...)

Arguments

fpp

KDE interpolator from cv_fastkde.

x_range

Optional range for plotting.

n_points

Number of points for plotting (default: 1000).

...

Additional plotting parameters.

Value

Called for its side effect (plotting). Returns NULL invisibly.

See Also

cv_fastkde

Examples


x <- matrix(rnorm(200), ncol = 1)
kde <- cv_fastkde(x)
fastkde_plot(kde$fpp)

Plot Bandwidth Selection Diagnostics for KDE

Description

Visualizes the bandwidth selection process for kernel density estimation, showing the LCV score as a function of bandwidth with the selected optimum marked.

Usage

fastkde_plot_bandwidth(kde, main = "Bandwidth Selection (LCV)",
                       xlab = NULL, ylab = NULL, ...)

Arguments

kde

A fastkde_result object returned by cv_fastkde.

main

Title for the plot.

xlab

Label for the x-axis (default: auto-generated).

ylab

Label for the y-axis (default: auto-generated).

...

Additional arguments passed to plot.

Value

Called for its side effect (plotting). Returns NULL invisibly.

Examples


x <- matrix(rnorm(500), ncol = 1)
hlist <- get_hlist(20, c(0.05, 2))
kde <- cv_fastkde(x, hlist)
fastkde_plot_bandwidth(kde)

Compute Confidence or Prediction Intervals

Description

Computes pointwise confidence intervals for the conditional mean or prediction intervals for new observations, using the mean and variance estimates from local polynomial regression.

Usage

fastlpr_interval(mu, sigma, alpha = 0.05, type = "confidence")

Arguments

mu

Mean regression result from cv_fastlpr (a list with field fpp_yhat).

sigma

Variance regression result from cv_fastlpr (a list with field fpp_yhat), or a numeric vector/matrix of standard deviations.

alpha

Significance level (default: 0.05 for 95% intervals).

type

Type of interval: "confidence" for the conditional mean or "prediction" for new observations (default: "confidence").

Value

List with lower and upper interval bounds.

See Also

cv_fastlpr, fastlpr_plot_interval

Examples


x <- matrix(runif(200), ncol = 1)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
mu <- cv_fastlpr(x, y)
sigma <- cv_fastlpr(x, (y - mu$yhat)^2)
ci <- fastlpr_interval(mu, sigma)

Plot regression results

Description

Visualizes fitted regression results.

Usage

fastlpr_plot(fpp_yhat, x_range = NULL, n_points = 1000, ...)

Arguments

fpp_yhat

Interpolant function or result object.

x_range

Optional range for plotting.

n_points

Number of points for plotting (default: 1000).

...

Additional plotting parameters.

Value

Called for its side effect (plotting). Returns NULL invisibly.

See Also

cv_fastlpr

Examples


x <- matrix(runif(200), ncol = 1)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
fit <- cv_fastlpr(x, y)
fastlpr_plot(fit$fpp_yhat)

Plot Confidence or Prediction Interval Bands

Description

Visualizes confidence or prediction interval bands for local polynomial regression estimates. Adds shaded interval regions to an existing plot.

Usage

fastlpr_plot_interval(ci, col = "green", alpha = 0.2, add = TRUE, ...)

Arguments

ci

An interval structure returned by fastlpr_interval.

col

Color for the interval band (default: "green").

alpha

Transparency level for the band (default: 0.2).

add

Logical; if TRUE (default), add to existing plot.

...

Additional arguments passed to plotting functions.

Value

Called for its side effect (plotting). Returns NULL invisibly.

See Also

fastlpr_interval, cv_fastlpr

Examples


set.seed(42)
x <- sort(runif(200))
y <- sin(2 * pi * x) + rnorm(200, sd = 0.3)
hlist <- get_hlist(20, c(0.01, 0.5))
regs <- cv_fastlpr(x, y, hlist)

Predict at new points

Description

Evaluates fitted regression at new predictor values.

Usage

fastlpr_predict(regs, x_new)

Arguments

regs

Regression results from cv_fastlpr.

x_new

New predictor values (matrix).

Value

Predicted response values.

See Also

cv_fastlpr

Examples


x <- matrix(runif(200), ncol = 1)
y <- sin(2 * pi * x) + rnorm(200, sd = 0.2)
fit <- cv_fastlpr(x, y)
x_new <- matrix(seq(0, 1, length.out = 50), ncol = 1)
yhat <- fastlpr_predict(fit, x_new)

Generate bandwidth candidates for cross-validation

Description

Creates a grid of bandwidth candidates for cross-validation. Port from MATLAB's get_hlist.m (unified API v2.0).

Usage

get_hlist(n, range, spacing = "logspace")

Arguments

n

Number of bandwidth candidates per dimension. Scalar: same number of points for all dimensions. Vector: specify number of points per dimension. Typical values: 20 for 1D, c(15, 15) for 2D.

range

Range of bandwidths (min, max) for each dimension. 1D: c(h_min, h_max) or matrix with 1 row. Multi-D: matrix with one row per dimension. Rule of thumb: h_min = 0.1 * sd(x), h_max = 1.0 * sd(x).

spacing

Spacing function type (default: "logspace"). "logspace": logarithmic spacing (better for exploring bandwidth scales). "linear": linear spacing.

Value

Matrix of bandwidth candidates (n_total x d). Each row is one bandwidth combination.

See Also

cv_fastlpr, cv_fastkde

Examples

# 1D: 20 bandwidths from 0.01 to 1 (log scale, default)
hlist <- get_hlist(20, c(0.01, 1))

# 2D: 10x10 grid of bandwidths
hlist <- get_hlist(10, rbind(c(0.01, 1), c(0.01, 1)))

# Linear spacing
hlist <- get_hlist(10, c(0.5, 0.6), "linear")

Get Rcpp Information

Description

Returns information about the Rcpp backend including version and available acceleration features.

Usage

get_rcpp_info()

Value

A list with Rcpp version and capabilities if available, NULL otherwise.

Examples

get_rcpp_info()

Check if Object is a fastkde_result

Description

Tests whether an object is of class fastkde_result.

Usage

is_fastkde_result(x)

Arguments

x

An R object to test.

Value

TRUE if x inherits from class "fastkde_result", FALSE otherwise.

Examples

is_fastkde_result(list())  # FALSE

Check if Object is a fastlpr_result

Description

Tests whether an object is of class fastlpr_result.

Usage

is_fastlpr_result(x)

Arguments

x

An R object to test.

Value

TRUE if x inherits from class "fastlpr_result", FALSE otherwise.

Examples

is_fastlpr_result(list())  # FALSE

Generate multi-dimensional grid

Description

Utility function to generate multi-dimensional grids.

Usage

multispace(x_min, x_max, N, space = "linear", type = "array", transpose = FALSE)

Arguments

x_min

Minimum values per dimension.

x_max

Maximum values per dimension.

N

Grid size per dimension.

space

Grid spacing: "linear" (default) or "logspace".

type

Output type: "array" (default) or "cell".

transpose

Whether to transpose output (default: FALSE).

Value

List of grid vectors.

Examples

grid <- multispace(0, 1, 50)

Check if Rcpp Acceleration is Available

Description

Tests whether the compiled Rcpp code is loaded and functional. This is useful for checking if C++ acceleration will be used.

Usage

rcpp_available()

Value

Logical. TRUE if Rcpp functions are available, FALSE otherwise.

Examples

rcpp_available()

Set default options

Description

Utility function to set a single default option field.

Usage

set_defaults(opt, field, default)

Arguments

opt

User-provided options list.

field

Field name to set.

default

Default value for the field.

Value

Merged options list.

Examples

opt <- list(order = 1)
opt <- set_defaults(opt, "kernel", "gaussian")

Z-score normalization

Description

Standardizes data to zero mean and unit variance.

Usage

zscore(x)

Arguments

x

Numeric vector or matrix.

Value

Standardized data with attributes for mean and standard deviation.

Examples

result <- zscore(rnorm(100, mean = 5, sd = 2))
mean(result$z)  # approximately 0