Federated Nonparametric Regression with Heterogeneous Clients
Abstract
Whether a federated predictor benefits an individual client depends on both population heterogeneity and estimation uncertainty. We study this question for Nadaraya--Watson regression in a triangular array with potentially different fitting and evaluation distributions. Each client transmits local kernel summaries, allowing the server to construct a covariate-density-weighted federated estimator without centralizing individual observations. A client combines its fitted local predictor with the federated predictor through a prescribed weight, and gain is the paired reduction in squared prediction loss on an independent audit observation. Exact identities characterize both the gain of the realized fitted pair and its repeated-fitting mean. We also establish pointwise inference for the federated estimator. A two-stage analysis of client gains separates fitting variability from audit variability, retains the covariance created when a client's observations enter both its local estimator and the common server estimator, and yields fixed-block simultaneous inference across clients. Robustness is examined under two perturbation models. A Kullback--Leibler neighborhood provides a variance-sensitive lower certificate in a regular positive-gain-variance regime, while an L2 neighborhood yields an exact least-favorable regression direction and robust value. Exact-model, vanishing-variance, and exact-zero-direction boundaries are kept separate because their scalar inputs are nonregular. The framework thus distinguishes decisions about a realized fitted pair from claims about the learning procedure under repeated fitting.
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BibTeX
@misc{jiang2026federated,
title = {{Federated Nonparametric Regression with Heterogeneous Clients}},
author = {Xiaoran Jiang and Anand N. Vidyashankar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32178},
eprint = {2610.32178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32178},
}
RIS
TY - UNPB
TI - Federated Nonparametric Regression with Heterogeneous Clients
AU - Xiaoran Jiang
AU - Anand N. Vidyashankar
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32178
UR - https://arxiv.org/abs/2610.32178
AB - Whether a federated predictor benefits an individual client depends on both population heterogeneity and estimation uncertainty. We study this question for Nadaraya--Watson regression in a triangular array with potentially different fitting and evaluation distributions. Each client transmits local kernel summaries, allowing the server to construct a covariate-density-weighted federated estimator without centralizing individual observations. A client combines its fitted local predictor with the federated predictor through a prescribed weight, and gain is the paired reduction in squared prediction loss on an independent audit observation. Exact identities characterize both the gain of the realized fitted pair and its repeated-fitting mean. We also establish pointwise inference for the federated estimator. A two-stage analysis of client gains separates fitting variability from audit variability, retains the covariance created when a client's observations enter both its local estimator and the common server estimator, and yields fixed-block simultaneous inference across clients. Robustness is examined under two perturbation models. A Kullback--Leibler neighborhood provides a variance-sensitive lower certificate in a regular positive-gain-variance regime, while an L_2 neighborhood yields an exact least-favorable regression direction and robust value. Exact-model, vanishing-variance, and exact-zero-direction boundaries are kept separate because their scalar inputs are nonregular. The framework thus distinguishes decisions about a realized fitted pair from claims about the learning procedure under repeated fitting.
ER -