antcc / rk-bfr

A functional regression framework built on Bayesian inference and RKHS's.

This package was developed as part of my master's thesis, which has since been rewritten and expanded as an article.

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rk-bfr

A Bayesian framework for functional linear and logistic regression models, built on the theory of RKHS's. An overview of the models is available on Chapter 3 here or Section 2 here.

Code structure

• The folder rkbfr contains the inference and prediction pipeline implemented, using the emcee MCMC sampler and following the style of the scikit-learn and scikit-fda libraries.
• The folder reference_methods contains the implementation of some functional algorithms used for comparison.
• The folder utils contains several utility files for experimentation and visualization.
• The experiments folder contains plain text files with numerical experimental results, as well as .csv and .npz files that facilitate working with them directly in Python.

Usage

There are some experiments (with both simulated and real data) available to test the performance of the models against other usual alternatives, functional or otherwise. The script results_cv.py runs the experiments with a cross-validation loop for our Bayesian models, while the script results_all.py runs the experiments for all hyperparameters without a cross-validation loop.

A typical execution can be seen in the launch.sh file, and additionally there are two Jupyter notebooks that demonstrate the usage of the code.

Code developed for Python 3.9.