论文标题
多维分段回归的有效算法
Efficient Algorithms for Multidimensional Segmented Regression
论文作者
论文摘要
我们研究了固定设计的基本问题{\ em多维分段回归}：给定函数$ f $的嘈杂样本，承诺在未知集的$ k $矩形集上进行分段线性，我们希望恢复$ f $ ful to noseSquared Orror中所需的准确性。我们在任何固定维度中为此问题提供了第一个样本和计算有效算法。我们的算法依赖于一种简单的迭代合并方法，该方法在多维环境中是新颖的。我们对合成数据集和真实数据集的实验评估表明，我们的算法具有竞争力，在某些情况下，我们的算法优于最先进的启发式方法。我们实现的代码可在\ url {https://github.com/avoloshinov/multidimensional-segented-regression}中获得。
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}.
