Handling Covariate Mismatch in Federated Linear Prediction
Abstract
Federated learning enables institutions to train predictive models collaboratively without sharing raw data, addressing privacy and regulatory constraints. In the standard horizontal setting, clients hold disjoint cohorts of individuals and collaborate to learn a shared predictor. Most existing methods, however, assume that all clients measure the same features. We study the more realistic setting of covariate mismatch, where each client observes a different subset of features, which typically arises in multicenter collaborations with no prior agreement on data collection. We formalize learning a linear prediction under client-wise MCAR patterns and develop two modular approaches tailored to the dimensional regime and communication budget. In the low-dimensional setting, we propose a plug-in estimator that approximates the oracle linear predictor by aggregating sufficient statistics to estimate the covariance and cross-moment terms. In higher dimensions, we study an impute-thenregress strategy: (i) impute missing covariates using any exchangeability-preserving imputation procedure, and (ii) fit a ridge-regularized linear model on the completed data. We provide asymptotic and finite-sample learning rates for our predictors, explicitly characterizing their behaviour with the global dimension, the client-specific feature partition, and the distribution of samples across sites.
Related
- Backward Conformal Prediction under Covariate Shift
- Finite-Sample Optimal Conformal Prediction Sets under Covariate Shift
- Sharp training-conditional coverage for conformal prediction under covariate shift
- PRESCCO: Efficient Prediction Intervals under a Right-Censored Covariate
- Sketched Calibration for Conformal Prediction under Covariate Shift
BibTeX
@misc{ayme2026handling,
title = {{Handling Covariate Mismatch in Federated Linear Prediction}},
author = {Alexis Ayme and Rémi Khellaf},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05490919v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Handling Covariate Mismatch in Federated Linear Prediction
AU - Alexis Ayme
AU - Rémi Khellaf
PY - 2026
DA - 2026/10/12
PB - HAL
UR - https://hal.science/hal-05490919v2
AB - Federated learning enables institutions to train predictive models collaboratively without sharing raw data, addressing privacy and regulatory constraints. In the standard horizontal setting, clients hold disjoint cohorts of individuals and collaborate to learn a shared predictor. Most existing methods, however, assume that all clients measure the same features. We study the more realistic setting of covariate mismatch, where each client observes a different subset of features, which typically arises in multicenter collaborations with no prior agreement on data collection. We formalize learning a linear prediction under client-wise MCAR patterns and develop two modular approaches tailored to the dimensional regime and communication budget. In the low-dimensional setting, we propose a plug-in estimator that approximates the oracle linear predictor by aggregating sufficient statistics to estimate the covariance and cross-moment terms. In higher dimensions, we study an impute-thenregress strategy: (i) impute missing covariates using any exchangeability-preserving imputation procedure, and (ii) fit a ridge-regularized linear model on the completed data. We provide asymptotic and finite-sample learning rates for our predictors, explicitly characterizing their behaviour with the global dimension, the client-specific feature partition, and the distribution of samples across sites.
ER -