fastLPR: Fast Local Polynomial Regression via NUFFT

Fast nonparametric regression and kernel density estimation using Non-Uniform Fast Fourier Transform (NUFFT) for MATLAB, Python, and R.

Features

• O(N + M log M) complexity - Scales efficiently to large datasets
• Multi-language support - MATLAB (reference), Python, and R implementations
• Flexible regression orders - Local constant (NW), local linear, local quadratic
• Automatic bandwidth selection - GCV for regression, LCV for density estimation
• Complex-valued data support - Handles complex predictors and responses
• Heteroscedastic variance estimation - Estimates conditional variance

Installation

MATLAB

cd fastLPR
fastLPR_setup

Python

cd fastLPR_py
uv pip install -e .

R

# From CRAN
install.packages("fastlpr")

# Or from source
setwd("fastLPR_R")
source("setup.R")

Quick Start

MATLAB

% 1D regression with automatic bandwidth selection
x = rand(500, 1);
y = sin(2*pi*x) + 0.1*randn(500, 1);
hlist = get_hList(20, [0.01, 1], @logspace);
opt.order = 1;  % Local linear
regs = cv_fastLPR(x, y, hlist, opt);
fastLPR_plot(regs.fpp_yhat);

Python

import numpy as np
from fastlpr import cv_fastlpr, get_hlist

x = np.random.rand(500, 1)
y = np.sin(2*np.pi*x) + 0.1*np.random.randn(500, 1)
hlist = get_hlist(20, [0.01, 1.0])
regs = cv_fastlpr(x, y, hlist, {'order': 1})

R

source("setup.R")
x <- matrix(runif(500), ncol=1)
y <- sin(2*pi*x) + 0.1*rnorm(500)
hlist <- get_hlist(20, c(0.01, 1.0))
regs <- cv_fastlpr(x, y, hlist, list(order=1))

Documentation

• MATLAB: See fastLPR/README.md and function help texts
• Python: See fastLPR_py/README.md and docstrings
• R: See fastLPR_R/README.md and roxygen2 documentation

Examples

Each implementation includes reproducible examples for the JSS paper figures:

fastLPR/example/reproduce_all_figures.m
fastLPR_py/examples/reproduce_all_figures.py
fastLPR_R/inst/examples/reproduce_all_figures.R

Citation

If you use fastLPR in your research, please cite:

@article{wang2025fastlpr,
  title = {{fastLPR}: Fast Local Polynomial Regression via {NUFFT} in {MATLAB}, {Python}, and {R}},
  author = {Wang, Ying and Li, Min and Paz-Linares, Deirel and Valdes-Sosa, Pedro A.},
  year = {2025},
  note = {Submitted},
  url = {https://github.com/rigelfalcon/fastLPR}
}

License

GPL-3.0-or-later. See LICENSE for details.

Authors

• Ying Wang (yingwangrigel@gmail.com)
• Min Li (minli.231314@gmail.com)
• Deirel Paz-Linares
• Pedro A. Valdes-Sosa