Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2107.00179
 Bibcode:
 2021arXiv210700179C
 Keywords:

 Mathematics  Statistics Theory;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Machine Learning;
 Statistics  Machine Learning;
 62F30