In this paper, we focus on distributed estimation and support recovery for
high-dimensional linear quantile regression. Quantile regression is a popular
alternative tool to the least squares regression for robustness against
outliers and data heterogeneity. However, the non-smoothness of the check loss
function poses big challenges to both computation and theory in the distributed
setting. To tackle these problems, we transform the original quantile
regression into the least-squares optimization. By applying a double-smoothing
approach, we extend a previous Newton-type distributed approach without the
restrictive independent assumption between the error term and covariates. An
efficient algorithm is developed, which enjoys high computation and
communication efficiency. Theoretically, the proposed distributed estimator
achieves a near-oracle convergence rate and high support recovery accuracy
after a constant number of iterations. Extensive experiments on synthetic
examples and a real data application further demonstrate the effectiveness of
the proposed method.

分布式估计和支持恢复在高维线性分位数回归中具有重要意义，本文通过将原始分位数回归转化为最小二乘优化问题，并应用双平滑方法，提出了一种新的分布式方法来解决此类问题，在保证计算和通信效率的同时能够实现接近 Oracle 收敛速度和高支持恢复精度的估计结果。通过对合成实例和真实数据应用的大量实验，验证了该方法的有效性。

分布式高维分位数回归：估计效率与支持恢复

Distributed High-Dimensional Quantile Regression: Estimation Efficiency  and Support Recovery

This paper addresses the problem of synchronizing orthogonal matrices over
directed graphs. For synchronized transformations (or matrices), composite
transformations over loops equal the identity. We formulate the synchronization
problem as a least-squares optimization problem with nonlinear constraints. The
synchronization problem appears as one of the key components in applications
ranging from 3D-localization to image registration. The main contributions of
this work can be summarized as the introduction of two novel algorithms; one
for symmetric graphs and one for graphs that are possibly asymmetric. Under
general conditions, the former has guaranteed convergence to the solution of a
spectral relaxation to the synchronization problem. The latter is stable for
small step sizes when the graph is quasi-strongly connected. The proposed
methods are verified in numerical simulations.

本文讨论如何在有向图上实现正交矩阵的同步化问题，提出了两种新算法，分别适用于对称图和非对称图，并经过数值模拟验证了其效果。