We study distributed schemes for high-dimensional sparse linear regression, based on orthogonal matching pursuit (OMP). Such schemes are particularly suited for settings where a central fusion center is connected to end machines, that have both computation and communication limitations. We prove that under suitable assumptions, distributed-OMP schemes recover the support of the regression vector with communication per machine linear in its sparsity and logarithmic in the dimension. Remarkably, this holds even at low signal-to-noise-ratios, where individual machines are unable to detect the support. Our simulations show that distributed-OMP schemes are competitive with more computationally intensive methods, and in some cases even outperform them.

翻译：我们研究了基于正交匹配追踪的高维稀疏线性回归分布式方案。此类方案特别适用于中央融合中心与端点机器相连接、且机器同时存在计算与通信限制的场景。我们证明，在适当假设条件下，分布式正交匹配追踪方案能以每台机器通信量随稀疏度线性增长、随维度对数增长的方式恢复回归向量的支持集。值得注意的是，即使在个体机器无法检测支持集的低信噪比条件下，该结论依然成立。仿真实验表明，分布式正交匹配追踪方案与计算密集型方法具有竞争力，在某些情况下甚至优于后者。