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

Comparison of packages

## 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

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**: alexandre.abbes@proton.me
**GitHub**: [alexandreabbes](https://github.com/alexandreabbes)