分散式网络上的分布式卷积秩回归
Distributed Convolutional Rank Regression over Decentralized Networks
- School of Mathematics and Statistics, Changchun University of Technology（长春工业大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究分散式网络上的卷积秩回归，提出含核平滑秩损失的分散式CRR框架，依赖本地与邻节点信息，实现隐私保护与高效通信，建立误差界与恢复保证，用广义共识ADMM求解，经实验验证性能良好。
AI中文摘要：
本文研究分散式分布式学习网络上的卷积秩回归（CRR）。我们提出了一种新颖的分散式CRR框架，通过求解具有核平滑秩损失的共识约束优化来获得估计器。该估计方案仅依赖本地节点数据和相邻节点共享的信息，实现隐私保护和高通信效率。对于异构网络设置，我们建立了分散式CRR估计器的有限样本误差界，并推导了稀疏分散式CRR LASSO估计器的精确支持恢复保证。为便于数值实现，采用广义共识ADMM有效解决所有网络节点的局部子问题。通过大量数值模拟和实际数据实验验证了所提方法的良好性能。
英文摘要：
This paper studies convolution rank regression (CRR) over decentralized distributed learning networks. We propose a novel decentralized CRR framework, in which estimators are obtained by solving consensus-constrained optimization with kernel-smoothed rank loss. The developed estimation scheme relies solely on local node data and information shared by neighboring nodes, thereby achieving privacy preservation and high communication efficiency. For heterogeneous network settings, we establish finite-sample error bounds for the decentralized CRR estimator and derive exact support recovery guarantees for the sparse decentralized CRR Lasso estimator. To facilitate numerical implementation, we adopt a generalized consensus ADMM to efficiently solve local subproblems across all network nodes. We verify the favorable performance of our developed approach via extensive numerical simulations and real-data experiments.
