Fast Local Polynomial Regression and Kernel Density Estimation.

fastlpr: Fast Local Polynomial Regression for R

NUFFT-accelerated local polynomial regression and kernel density estimation for R. This is the R port of the fastLPR MATLAB/Python toolbox, achieving O(N + M log M) computational complexity through Non-Uniform Fast Fourier Transform (NUFFT) with Gaussian gridding.

Features

• Fast: 20-60x faster than ks package for KDE, 100-1000x faster than naive implementations
• Flexible: Supports 1D/2D/3D data, complex-valued responses, heteroscedastic variance estimation
• Automatic: GCV/LCV-based bandwidth selection with 1-SE rule for robustness
• Complete: Confidence intervals, DOF estimation, multiple polynomial orders (0/1/2)

Installation

From Source (Development)

# Clone repository and navigate to fastLPR_R
setwd("path/to/fastLPR_R")

# Option 1: Source setup script (for development)
source("setup.R")

# Option 2: Install as package (recommended)
# From command line:
# R CMD INSTALL .

Dependencies

Required:

• R >= 4.0.0
• Matrix (>= 1.0.0)
• Rcpp (>= 1.0.0)
• RcppArmadillo (>= 0.10.0)

Suggested:

• testthat (>= 3.0.0) - for testing
• R.matlab - for cross-validation against MATLAB references
• akima, interp, fields - for additional interpolation methods

Quick Start

Kernel Density Estimation (KDE)

library(fastlpr)

# 1D KDE
set.seed(42)
x <- matrix(rnorm(500), ncol = 1)
hlist <- get_hlist(20, c(0.05, 0.5), "logspace")
opt <- list(order = 0)  # order=0 for KDE
kde <- cv_fastkde(x, hlist, opt)

# Selected bandwidth
print(kde$h)

# 2D KDE
x2d <- matrix(rnorm(2000), ncol = 2)
hlist2d <- get_hlist(c(10, 10), rbind(c(0.1, 1), c(0.1, 1)), "logspace")
kde2d <- cv_fastkde(x2d, hlist2d, list(order = 0))

Local Polynomial Regression

# 1D Local Linear Regression
x <- matrix(runif(500), ncol = 1)
y <- sin(2 * pi * x) + 0.1 * matrix(rnorm(500), ncol = 1)
hlist <- get_hlist(20, c(0.01, 0.5), "logspace")

opt <- list(
  order = 1,       # 0=Nadaraya-Watson, 1=local linear, 2=local quadratic
  calc_dof = TRUE  # Enable DOF estimation for GCV
)
regs <- cv_fastlpr(x, y, hlist, opt)

# Results
print(regs$gcv_yhat$h)  # Selected bandwidth
yhat <- regs$yhat       # Fitted values

Heteroscedastic Variance Estimation

# Mean estimation
opt_mean <- list(order = 1, calc_dof = TRUE)
res_mean <- cv_fastlpr(x, y, hlist, opt_mean)

# Variance estimation using squared residuals
residuals_sq <- (y - res_mean$yhat)^2
opt_var <- list(order = 1, calc_dof = TRUE, y_type_out = "variance")
res_var <- cv_fastlpr(x, residuals_sq, hlist, opt_var)

Package Structure

fastLPR_R/
├── R/                          # Source files (26 files)
│   ├── cv_fastlpr.R           # Main regression API
│   ├── cv_fastkde.R           # Main KDE API
│   ├── fastlpr_*.R            # Core algorithm components
│   ├── nufft.R                # NUFFT implementation
│   ├── lwp_estimator.R        # Local polynomial estimator
│   └── utils.R                # Utility functions
├── src/                        # C++ acceleration (Rcpp/RcppArmadillo)
├── inst/
│   ├── examples/              # JSS paper figure reproduction scripts
│   │   ├── example_fig2_fastkde.R
│   │   ├── example_fig3_boundary_comparison.R
│   │   ├── example_fig4_complex.R
│   │   ├── example_fig5_heteroscedasticity.R
│   │   ├── example_fig6_applications.R
│   │   └── reproduce_all_figures.R
│   └── benchmarks/            # Performance comparison scripts
│       ├── benchmark_tab4_kde_comparison.R
│       ├── benchmark_kde_large_scale.R
│       └── benchmark_lpr_npregfast.R
├── tests/
│   └── testthat/              # Test suite
│       ├── test-cross-validation.R  # 10-test MATLAB cross-validation
│       └── test-*.R                 # Component tests
├── man/                        # Documentation (roxygen2)
├── data/                       # Example datasets
├── dev/                        # Development files (excluded from build)
├── DESCRIPTION                 # Package metadata
├── NAMESPACE                   # Exported functions
└── LICENSE                     # GPL-3

Examples (JSS Paper Figures)

Reproduce all figures from the JSS paper:

# Run all figure scripts
source(system.file("examples", "reproduce_all_figures.R", package = "fastlpr"))

# Or run individual figures
source(system.file("examples", "example_fig2_fastkde.R", package = "fastlpr"))

Benchmarks

Performance comparison with existing R packages:

# Run benchmark scripts
source(system.file("benchmarks", "benchmark_tab4_kde_comparison.R", package = "fastlpr"))

KDE: fastlpr vs ks package (N=50,000)

• fastlpr: 0.34s
• ks: 19.98s
• Speedup: 59x

LPR: fastlpr vs statsmodels (Python, N=5,000)

• Naive O(N²): 31.7s
• fastlpr O(N log N): 0.03s
• Speedup: 1000x+

Testing

Run the test suite:

# Using testthat
setwd("fastLPR_R")
testthat::test_dir("tests/testthat")

# Or via devtools
devtools::test()

Cross-validation results (10 tests against MATLAB reference):

* For KDE tests (order=0), LCV MaxErr shown in GCV column; All metrics must pass

API Reference

Main Functions

Options

opt <- list(
  order = 1,                # Polynomial order: 0, 1, or 2
  kernel_type = "gaussian", # Kernel: "gaussian" or "epanechnikov"
  N = 100,                  # Grid size per dimension
  accuracy = 6,             # NUFFT accuracy (1-12)
  calc_dof = TRUE,          # Compute DOF for GCV
  dstd = 0                  # Std devs for 1-SE rule (0 = minimum GCV)
)

Citation

If you use fastlpr in your research, please cite:

@article{fastlpr2025,
  title = {fastLPR: Fast Local Polynomial Regression with NUFFT Acceleration},
  author = {Wang, Ying and Li, Min},
  journal = {Journal of Statistical Software},
  year = {2025},
  note = {R package version 1.0.0}
}

License

GPL-3

Related Packages

• fastLPR (MATLAB) - Reference implementation
• fastlpr (Python) - Python port.