  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.
