分布式网络下高效隐私保护的卷积秩回归方法
Distributed Convolutional Rank Regression over Decentralized Networks
- 基于邻域信息与核平滑秩损失的分布式优化框架
- 在异构网络中实现误差有界且支持精确恢复
- 适合注重隐私与通信效率的分布式学习场景
本文研究去中心化分布式学习网络中的卷积秩回归（CRR）。提出一种新型去中心化CRR框架，通过求解带共识约束的优化问题并采用核平滑秩损失获得估计器。该方法仅依赖本地节点数据及邻近节点共享信息，实现隐私保护与高通信效率。针对异构网络设置，建立了去中心化CRR估计器的有限样本误差界，并推导出稀疏去中心化CRR Lasso估计器的精确支撑恢复保证。为促进数值实现，采用广义共识ADMM高效求解各节点的局部子问题。通过大量数值模拟与真实数据实验验证了所提方法的良好性能。
原文摘要 · Abstract (English)
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.
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