Optimal Distributed Nonparametric Regression
Gottfried E. Noether Award Lecture
Presented at the Joint Statistical Meetings in Toronto, August 2023
Abstract: Distributed statistical estimation and inference have gained significant importance due to the prevalence of data distributed across various locations in many applications. The distributed setting arises from constraints related to data size, privacy considerations, or security concerns. These scenarios are commonly encountered in diverse fields such as medicine, finance, and business.
In this talk, we discuss optimal distributed nonparametric regression in a decision theoretical framework, considering constraints on communication or privacy. By establishing minimax rates of convergence, we quantify the tradeoff between communication/privacy costs and statistical accuracy, particularly under independent communication protocols. Additionally, we develop estimation procedures that achieve rate-optimality. The results we present uncover novel and interesting phenomena, suggesting promising avenues for further exploration.
Papers:
- Cai, T.T., Chakraborty, A., & Vuursteen, L. (2023).
Optimal federated learning for nonparametric regression with heterogenous distributed differential privacy constraints.
Manuscript. - Cai, T. T. & Wei, H. (2022).
Distributed nonparametric regression: Optimal rate of convergence and cost of adaptation.
The Annals of Statistics, 50, 698-725.