将数据分片后分布式压缩，显著降低大样本回归计算成本。
Distributed Sketching on Data Partitions for OLS Regression
- 对数据分片分别进行压缩，再平均估计结果
- 分片间协方差差异小时，误差接近全局压缩方案
- 适合大规模数据下需降低通信与计算开销的场景
本文研究分布式最小二乘（OLS）回归中的分布式压缩方法，该方法将大数据集的小型压缩表示分发到多台机器上，各自构建OLS估计量后再取平均。与以往在全数据集上压缩的研究不同，本文考虑在数据分片上进行压缩，进一步降低计算开销。在固定设计设定下，我们精确刻画了平均后估计量的额外损失。结果表明，当各子集协方差之间的差异较小时，该损失与全局压缩的已有损失水平相当。
原文摘要 · Abstract (English)
This paper studies distributed sketching for ordinary least squares (OLS) regression, an approach that distributes small sketches of a large data set over multiple machines to separately construct OLS estimators and average them. Unlike prior studies that consider sketching on the whole data set, we consider sketching on partitioned subsets to further reduce computational cost. Under the fixed design setting, we characterize the exact excess loss of the averaged OLS estimator. Results show that this loss is comparable to the established loss for sketching on the whole data set when the divergence among subset covariances is small.
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