Efficient Algorithms for Multidimensional Segmented Regression

• URL: http://arxiv.org/abs/2003.11086v1
• Date: Tue, 24 Mar 2020 19:39:34 GMT
• Title: Efficient Algorithms for Multidimensional Segmented Regression
• Authors: Ilias Diakonikolas and Jerry Li and Anastasia Voloshinov
• Abstract summary: We study the fundamental problem of fixed design em multidimensional regression. We provide the first sample and computationally efficient algorithm for this problem in any fixed dimension. Our algorithm relies on a simple merging iterative approach, which is novel in the multidimensional setting.
• Score: 42.046881924063044
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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}.

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