Distributed computing is critically important for modern statistical
analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with
excellent statistical, computation, and communication efficiency. In the DQN
method, no Hessian matrix inversion or communication is needed. This
considerably reduces the computation and communication complexity of the
proposed method. Notably, related existing methods only analyze numerical
convergence and require a diverging number of iterations to converge. However,
we investigate the statistical properties of the DQN method and theoretically
demonstrate that the resulting estimator is statistically efficient over a
small number of iterations under mild conditions. Extensive numerical analyses
demonstrate the finite sample performance.

开发了具有卓越统计分析、计算和通信效率的分布式拟牛顿（DQN）框架，无需 Hessian 矩阵倒置或通信，在小数次迭代下提供了统计效率的结果，强调与现有方法的差别在于对统计学性质的调查。

大规模分布式学习中的拟牛顿更新

Quasi-Newton Updating for Large-Scale Distributed Learning

We propose an $\ell_1$-penalized estimation procedure for high-dimensional
linear mixed-effects models. The models are useful whenever there is a grouping
structure among high-dimensional observations, i.e. for clustered data. We
prove a consistency and an oracle optimality result and we develop an algorithm
with provable numerical convergence. Furthermore, we demonstrate the
performance of the method on simulated and a real high-dimensional data set.

本研究提出了一种针对高维线性混合效应模型的 $\ell_1$- 惩罚估计过程，该模型对于高维观测中存在分组结构的数据非常有用。我们证明了一致性和优化性结果，并开发了一种具有可证明数值收敛性的算法。此外，我们还在模拟和实际高维数据集上展示了该方法的性能。