This Python library implements convex regression algorithms of various papers.

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ALGORITHMS

Convex Nonparametric Least-Squares (CNLS)
algorithm/cnls/cnls.py

Convex Optimization, Section 6.5.5,
Stephen Boyd, Lieven Vandenberghe,
Cambridge University Press, 2004 (book).

Least-Squares Partition Algorithm (LSPA)
algorithm/lspa/lspa.py

Convex Piecewise-Linear Fitting,
Alessandro Magnani, Stephen P. Boyd,
Optimization and Engineering, vol.10, 2009 (paper).

Convex Adaptive Partitioning (CAP), and FastCAP
algorithm/cap/cap.py

Multivariate Convex Regression with Adaptive Partitioning,
Lauren A. Hannah, David B. Dunson,
JMLR, vol.14, 2013 (paper, MATLAB code)

Partitioning Convex Nonparametric Least-Squares (PCNLS) with uniformly random Voronoi partition
algorithm/pcnls/pcnls_voronoi.py

Near-Optimal Max-Affine Estimators for Convex Regression,
Gabor Balazs, Andras Gyorgy, Csaba Szepesvari,
AISTATS, 2015 (paper, MATLAB code).

Adaptive Max-Affine Partitioning (AMAP)
algorithm/amap/amap.py

Convex Regression: Theory, Practice, and Applications, Section 6.2.3,
Gabor Balazs,
PhD Thesis, University of Alberta, 2016 (thesis, MATLAB code).

Adaptively Partitioning Convex Nonparametric Least-Squares (APCNLS)
algorithm/apcnls/apcnls.py

Adaptively Partitioning Max-Affine Estimators for Convex Regression,
Gabor Balazs,
AISTATS, 2022 (paper).

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PYTHON ENVIRONMENT

The installation of a minimal virtual environment to show the requirements of running the code.

python3 -m venv .../pyenv  # creating empty virtual environment
source .../pyenv/bin/activate  # activating the virtual environment

pip install --upgrade pip
pip install --upgrade setuptools

pip install numpy scipy osqp

# Jupyter notebook (Optional):
pip install joblib pandas 
pip install widgetsnbextension jupyter matplotlib

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UNIT TESTING

For examples, see the doctests in the files mentioned in the ALGORITHMS section above.

All the doctests can be run by using the nose package:

source .../pyenv/bin/activate  # if not done yet
pip install pytest
cd .../cvxreg  # go to the root directory of this project
PYTHONPATH=. pytest --doctest-modules

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EXPERIMENTS

There is a Jupyter notebook ipynb/cvxreg_synt.ipynb which provides basic experimenting on synthetic convex regression problems.