2021/07/01 by T. Tony Cai, Cai, T. Tony, Hongji Wei +1 · 2 citations
Computer Science · Mathematics · #62F30 #Distributed #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Parallel #Statistical Methods and Inference #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2107.00179
openalex publication_date 2021/07/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/01
Distributed minimax estimation and distributed adaptive estimation under communication constraints for Gaussian sequence model and white noise model are studied. The minimax rate of convergence for distributed estimation over a given Besov class, which serves as a benchmark for the cost of adaptation, is established. We then quantify the exact communication cost for adaptation and construct an optimally adaptive procedure for distributed estimation over a range of Besov classes. The results demonstrate significant differences between nonparametric function estimation in the distributed setting and the conventional centralized setting. For global estimation, adaptation in general cannot be achieved for free in the distributed setting. The new technical tools to obtain the exact characterization for the cost of adaptation can be of independent interest.