Perfectly fits a polynomial hypersurface to any dataset. A fairly straightforward mathematical exercise, this gave me a fun problem to work on during covid.

This algorithm is a multivariable generalization of polynomial interopolation, which is generally not the best strategy for multivariate interpolation, but it does serve as a demonstration for polynomial completeness.

This program is run from the command line by running the file overfit.py. It takes an input dataset as a csv file containing m rows (datapoints) of n columns each. The first n-1 elements in each row represent that datapoint's coordinates, and the nth element is the value at that point. The next arguments can be either a set of coordinates to interpolate or a command to plot the polynomial with a given window.

This repository includes some (very) small example data. I built this less than a year into college before I understood portability, but this doesn't use any particularly specialized packages. I'm able to run on an intel-based Macbook running MacOS Ventura with Python 3.9.6, matplotlib 3.7.2 and numpy 1.25.2 with the following commands. Since numpy is a matplotlib prereq, only installing matplotlib should suffice.

python -m venv venv
source venv/bin/activate
pip install matplotlib
git clone https://github.com/cooper6558/Overfit.git
cd Overfit
python overfit.py planar_data.csv plot 0 4 0 4
python overfit.py planar_data.csv 2.5
> Prediction: 2.367188
python overfit.py data.csv 1 2 3
> Prediction: 5.687369

If you think this code looks like it was written by a college freshman, that's because it was. I was revisiting this repository three years later and decided I might as well keep it up, so I wrote this quick readme and fixed some things to make the code run without crashing, but I won't be spending any more time on this project.