Feature-distributed data, referred to data partitioned by features and stored
across multiple computing nodes, are increasingly common in applications with a
large number of features. This paper proposes a two-stage relaxed greedy
algorithm (TSRGA) for applying multivariate linear regression to such data. The
main advantage of TSRGA is that its communication complexity does not depend on
the feature dimension, making it highly scalable to very large data sets. In
addition, for multivariate response variables, TSRGA can be used to yield
low-rank coefficient estimates. The fast convergence of TSRGA is validated by
simulation experiments. Finally, we apply the proposed TSRGA in a financial
application that leverages unstructured data from the 10-K reports,
demonstrating its usefulness in applications with many dense large-dimensional
matrices.

该论文提出了一种两阶段松弛贪心算法（TSRGA），用于对特征分布数据应用多元线性回归分析。TSRGA 的主要优势是其通信复杂度不依赖于特征维度，使其能够高度扩展到非常大的数据集。此外，对于多元响应变量，TSRGA 可以用于得到低秩系数估计。通过模拟实验验证了 TSRGA 的快速收敛性。最后，我们将所提出的 TSRGA 应用于金融应用中，利用来自 10-K 报告的非结构化数据，展示了其在密集大维矩阵的众多应用中的实用性。