Efficient Algorithms for Multidimensional Segmented Regression

arXiv2003.11086MaRDI QIDQ6337358

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Publication date: 24 March 2020

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}.

Has companion code repository: https://github.com/avoloshinov/multidimensional-segmented-regression

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