🤖 AI Summary
This work addresses the challenges of data heterogeneity and communication efficiency in decentralized networks by proposing a privacy-preserving distributed Convolutional Rank Regression (CRR) estimation method. The approach leverages a kernel-smoothed rank loss combined with consensus constraints, enabling each node to train its model using only local data and information from neighboring nodes. An efficient solution is achieved via a generalized consensus ADMM algorithm. Theoretically, this study establishes the first finite-sample error bounds for decentralized CRR and provides sharp support recovery guarantees for sparse CRR LASSO estimators. Experimental results demonstrate that the proposed method consistently outperforms existing approaches in terms of estimation accuracy, communication overhead, and privacy preservation.
📝 Abstract
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.