# Combinatorial optimization of the coefficient of determination

arXiv: https://arxiv.org/abs/2410.09316 · HTML: https://mlsanity.com/paper/2410.09316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 43 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 2 of 2)

- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [Dynamic Planar Convex Hull](https://mlsanity.com/paper/1902.11169/) (2019)

## Abstract (arXiv)

Robust correlation analysis is among the most critical challenges in statistics. Herein, we develop an efficient algorithm for selecting the k- subset of n points in the plane with the highest coefficient of determination left( R2 right). Drawing from combinatorial geometry, we propose a method called the textitquadratic sweep that consists of two steps: (i) projectively lifting the data points into mathbb R5 and then (ii) iterating over each linearly separable k-subset. Its basis is that the optimal set of outliers is separable from its complement in mathbb R2 by a conic section, which, in mathbb R5, can be found by a topological sweep in Theta left( n5 log n right) time. Although key proofs of quadratic separability remain underway, we develop strong mathematical intuitions for our conjectures, then experimentally demonstrate our method's optimality over several million trials up to n=30 without error. Implementations in Julia and fully seeded, reproducible experiments are available at https://github.com/marc-harary/QuadraticSweep.