Efficient Algorithms for Multidimensional Segmented Regression

TL;DR

This paper introduces the first efficient algorithm for multidimensional segmented regression, capable of recovering piecewise linear functions from noisy data with theoretical guarantees and practical performance.

Contribution

It presents a novel iterative merging algorithm for fixed-dimensional multidimensional segmented regression, with proven efficiency and accuracy.

Findings

Algorithm is computationally efficient and theoretically sound.

Experimental results show competitive or superior performance to existing heuristics.

Code implementation is publicly available for reproducibility.

Abstract

We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a desired accuracy in mean-squared error. We provide the first sample and computationally efficient algorithm for this problem in any fixed dimension. Our algorithm relies on a simple iterative merging approach, which is novel in the multidimensional setting. Our experimental evaluation on both synthetic and real datasets shows that our algorithm is competitive and in some cases outperforms state-of-the-art heuristics. Code of our implementation is available at \url{https://github.com/avoloshinov/multidimensional-segmented-regression}.