'Constrained Quantile Regression with B-Splines'

Quantile regression with B-splines under shape constraints. The initial version with cubic splines is now augmented with splines of degree 1 to 4. Constraints for degrees 3 (monotone) and 4 (monotone and convex) use the Karlin-Studden SOCP characterization for the sign of the polynomial, while other constraints applied at the knots are added as linear problems. The method for cubic splines is described in 'Abbes (2026)' . Other formulations are simple consequences of the other given references. All B-spline and polynomial functions have been rewritten for consistency. This package provides an original B-spline library for conversion between PP-form and B-spline representation, evaluation, differentiation, callable and non-callable objects, print human readable pp forms, view basis, all based on "De Boor\'s" theory. It also extends to multiple knots to catch up singularities. This feature is robust in the package including for constrained regression. This R implementation is intended for demonstration and prototyping. An equivalent Python package is available at < https://pypi.org/project/BsplineQuantRegpy/>.

BsplineQuantReg

Constrained Quantile Regression with B-Splines (Degrees 1 to 4)

This package is available on CRAN.

Features

• Quantile regression for any tau in (0,1)
• B-splines of degree 1 to 4 (linear to quartic)
• Monotonicity constraints (increasing or decreasing)
• Convexity constraints (convex or concave)
• Third derivative constraints for cubic and quartic splines
• Karlin-Studden SOCP formulation for rigorous shape constraints
• Partial constraints (per interval or per knot)
• Polynomial coefficient export
• Conversion between PP-form and B-spline representation
• Callable and non-callable spline/pp objects
• View Bspline basis
• Differentiable Bspline or Basis
• Displays coefficients in human readable form, local/canonical basis
• Robust knots multiplicity management (for lower regularity at knots, such as shocks)

Installation

From CRAN (stable, recommended)

install.packages("BsplineQuantReg")

From GitHub (development version)

devtools::install_github("alexandreabbes/BsplineQuantReg")

System Requirements

Linux Users

On Linux systems, the packages CVXR and CLARABEL require the Rust compiler and Cargo package manager to be installed.

Ubuntu/Debian:

sudo apt-get install cargo rustc

Fedora and other linux dist.

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh -
source ~/.cargo/env

Verify installation:

rustc --version
cargo --version

After installing Rust and Cargo, restart R and install the package:

install.packages("BsplineQuantReg")

Windows Users

Windows users do not need to install Rust separately. The package uses pre-compiled binaries available on CRAN.

Graphical Interface (Shiny)

This package includes an interactive Shiny interface that allows you to manage most of the functions without writing code.

Launch the GUI

library(BsplineQuantRegGui)
run_gui()

The interface will open in your default browser.

Features of the GUI

Load data (CSV, Excel, built-in datasets)

Configure spline parameters (degree, knots)

Apply shape constraints (monotonicity, convexity, third derivative)

Define constraints per region interactively

Run quantile regression with various solvers

Visualize results with interactive plots

Export reproducible R code

Run built-in demos

View Bspline Basis, derivatives

Manage knots multiplicity

Docker Deployment

A Docker image is available for easy deployment: bash bash``` docker pull ghcr.io/alexandreabbes/bsplinequantreggui:latest docker run -p 3838:3838 ghcr.io/alexandreabbes/bsplinequantreggui:latest

Then open http://localhost:3838 in your browser.


### Installation

```r
# Install from GitHub
remotes::install_github("alexandreabbes/bsplinequantreggui")

# Or with pak
pak::pkg_install("alexandreabbes/bsplinequantreggui")

Related Packages

R Packages

Comparison with cobs

The cobs package (Constrained B-Splines with linear or quadratic splines) is the closest to this package.

Python package

Python version: https://pypi.org/project/BsplineQuantRegpy/

Matlab core

You may take a look here for a glimpse at the initial matlab code. https://github.com/alexandreabbes/Constrained-Quantile-Regression-with-cubic-splines/tree/matlab `

Performance Notice

This R package is intended for demonstration, prototyping, and educational purposes. Due to the current implementation (pure R with CVXR) the package is almost 5 times slower than its Python counterpart (benchmark test), but much (10 times maybe) faster than the matlab one. B-spline quantile regression with constraints involves solving SOCP problems, and the R implementation does not yet leverage optimized linear algebra libraries.

Future Improvements

• Optimize the B-spline basis computation
• Improve the API based on user feedback

Getting Started

library(BsplineQuantReg)

# Generate sample data
set.seed(42)
x <- seq(0, 1, length.out = 100)
y <- 2*x + 0.5*sin(6*pi*x) + 0.05*rnorm(100)
knots <- quantile(x, probs = seq(0, 1, length.out = 10))

# Quantile regression with cubic spline and increasing constraint
fit <- SplineCubicQuant(x, y, knots, tau = 0.5, monot = 1)

# Evaluate the spline
x_eval <- seq(0, 1, length.out = 200)
#y_eval <- spline_eval(fit, x_eval) # deprecated now
y_eval <- fit(x_eval) # the fit is now callable

Demos

# List available demos
demo(package = "BsplineQuantReg")

# Run a specific demo
demo("comprehensive", package = "BsplineQuantReg")
demo("temperature", package = "BsplineQuantReg")

Citation

If you use this package in your research, please cite:

@Article{Abbes2025,
  author  = {Alexandre Abbes},
  title   = {Constrained Quantile Regression with Cubic B-Splines under Shape Constraints},
  year    = {2025},
  doi     = {10.5281/zenodo.17427913}
}

## Bug Reports

Please report issues on GitHub: https://github.com/alexandreabbes/BsplineQuantReg/issues