# Efficient Algorithms for Multidimensional Segmented Regression

arXiv: https://arxiv.org/abs/2003.11086 · HTML: https://mlsanity.com/paper/2003.11086/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Data-Driven Subgroup Identification for Linear Regression](https://mlsanity.com/paper/2305.00195/) (2023)
- [An Efficient Data Analysis Method for Big Data using Multiple-Model Linear Regression](https://mlsanity.com/paper/2308.12691/) (2023)

## Abstract (arXiv)

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 urlhttps://github.com/avoloshinov/multidimensional-segmented-regression.