Distributed Regression Imputation for Distributed Cluster-Type Missing Data

To solve the problems of both low imputation precision and high time costs, the trimmed scores regression (TSR) method has been proposed as an imputation method for clustering data with missing values, where clustering pursues homogeneity within clusters and heterogeneity between clusters. However, as a centralized method, the TSR suffers from critical computational bottlenecks in large-scale scenarios. To overcome these limitations, we propose the distributed TSR (DTSR) method within a distributed framework. Two distributed methods, namely the DEMI and the DRPCA, as well as the TSR, are used as benchmarks. Through simulation and real-data analysis, we evaluate the DTSR from the perspectives of imputation accuracy and computational efficiency. The results show that the DTSR maintains high imputation accuracy equivalent to the TSR and significantly reduces running time compared with the centralized version. Meanwhile, the DTSR exhibits similar running time to both the DEMI and the DRPCA, achieving a better balance between accuracy and efficiency.