BsplineQuantRegpy 1.0.4

Quantile Regression with Constrained B-Splines

Quantile Regression with Constrained Splines

Python implementation of quantile regression with constrained splines (degrees 1-4). Degrees 1-3 are based on the article "Quantile regression with cubic splines under shape constraints" by Alexandre Abbes, while degree 4 is a natural consequence of the cited references.

Associated packages

Package	Langage	Description	Lien
BsplineQuantReg	R	Splines cubiques contraintes, self-contained	CRAN
cobs	R	Constrained B-Splines (linéaires et quadratiques)	CRAN
quantreg	R	Quantile Regression	CRAN
quantreg	Python	Quantile Regression	statmodels or PyPI
Ce package	Python	Splines de degrés 1 à 4 contraintes	GitHub

Comparison of packages

Fonctionnality	cobs (R)	BsplineQuantReg (R)	BsplineQuantRegpy (Python)
Linear Splines	✅	❌	✅
Quadratic Splines	✅	❌	✅
Cubic Splines	❌	✅	✅
Quartic Splines	❌	❌	✅
Contraints at knots	✅	✅	✅
Over the whole interval	❌	✅	✅
Region constraints	❌	✅	✅
Third derivative	❌	❌	✅
Gui	❌	❌	✅
Self-contained for Bsplines	❌	✅	❌ (utilise SciPy)

## Features

-  Quantile regression with splines of degree 1 to 4
-  Constraints on derivatives (monotonicity, convexity, third derivative)
-  Constraints valid over the entire interval or selected regions
-  Graphical interface for interactive testing (Tkinter)
-  Multiple solvers support (CLARABEL, ECOS, SCS, MOSEK)

##  Installation

### Python

```bash
# From PyPI
pip install BsplineQuantRegpy

# Or from source
git clone https://github.com/alexandreabbes/BsplineQuantRegpy.git
cd BsplineQuantRegpy
pip install -e .

R

# From CRAN
install.packages("BsplineQuantReg")

Links

• Python Repository: https://github.com/alexandreabbes/BsplineQuantRegpy
• R Repository: https://github.com/alexandreabbes/BsplineQuantReg
• R CRAN Package: https://cran.r-project.org/package=BsplineQuantReg
• DOI: 10.5281/zenodo.17427913

File Structure

Graphical Interface

• Quantr_eg_tk.py - Tkinter GUI for interactive parameter testing (spline degree, knots, derivative constraints)

Main Algorithms

File	Description
SplineCubicQuant.py	Cubic splines with constraints on 1st, 2nd, and 3rd derivatives
SplineQuarticQuant.py	Quartic splines with exact constraints over the entire interval
SplineQuadraticQuant.py	Quadratic splines with constraints on 1st and 2nd derivatives
SplineLinearQuant.py	Linear splines with constraints on 1st derivative '
quantile_spline.py	Unified function for regresion with any degree 1-4 and constraints

Examples and Data

• example_temerature.py - Replication of the test on global warming (temperatures , data in temp.xls)
• examples/ - Additional usage examples

Quick Start

from splinequantreg import SplineCubicQuantile
import numpy as np
Quickstart
Quickstart2

# Or
# Generate data
x = np.linspace(0, 1, 100)
y = 3*x + 0.2*np.sin(10*np.pi*x) + 0.1*np.random.randn(100)
knots = np.quantile(x, np.linspace(0, 1, 11))

# Fit with monotonicity constraint
result = SplineCubicQuantile(x, y, knots, tau=0.5, monot=1)

# Evaluate
x_eval = np.linspace(0, 1, 200)
y_eval = result(x_eval)

Or launch the GUI:

from splinequantreg import run_gui
run_gui()

Prerequisites

Python

pip install numpy scipy pandas matplotlib cvxpy

``

Citation

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

@article{abbes2025quantile,
  title={Quantile regression with cubic polynomial splines under shape constraints with applications},
  author={Abbes, Alexandre},
  year={2025},
  doi={10.5281/zenodo.17427913}
}


## Contributions

Contributions are welcome! Feel free to:

- Open an [issue](https://github.com/alexandreabbes/BsplineQuantRegpy/issues)
- Submit a [pull request](https://github.com/alexandreabbes/BsplineQuantRegpy/pulls)
- Suggest improvements

## License

This project is licensed under the GPL-v3 License - see the [LICENSE](LICENSE) file for details.

## AI Assistance

This project was carried out with the assistance of **DeepSeek** ([https://deepseek.com/](https://deepseek.com/)), which helped the developer with:
- Implementing constrained spline algorithms from MATLAB to Python
- Translating mathematical concepts into Python code
- Structuring programs and documentation

DeepSeek is a language model developed by 深度求索 [1].

[1] DeepSeek-AI. (2024). DeepSeek-V3 Technical Report. arXiv:2412.19437.

## References

- Abbes, A. (2025). Quantile regression with cubic polynomial splines
under shape constraints with applications. doi:10.5281/zenodo.17427913
- He, X., & Shi, P. (1998). Monotone B-spline smoothing. *Journal of the American Statistical Association*, 93(442), 643-650.
- Karlin, S., & Studden, W.J. (1966). *Tchebycheff Systems: With Applications in Analysis and Statistics*. Interscience Publishers.
- Papp, D., & Alizadeh, F. (2014). Shape-Constrained Estimation Using Nonnegative Splines. *Journal of Computational and Graphical Statistics*, 23(1), 211-231.


## Contact

**Author**: Alexandre Abbes
**Email**: [e-mail]
**GitHub**: [alexandreabbes](https://github.com/alexandreabbes)