# Handling Covariate Mismatch in Collaborative Linear Prediction

arXiv: https://arxiv.org/abs/2602.02083 · HTML: https://mlsanity.com/paper/2602.02083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)](https://mlsanity.com/paper/1306.2119/) (2013)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression](https://mlsanity.com/paper/1602.05419/) (2016)
- [Asymptotics of Ridge (less) Regression under General Source Condition](https://mlsanity.com/paper/2006.06386/) (2020)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices](https://mlsanity.com/paper/1912.10754/) (2019)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Linear predictor on linearly-generated data with missing values: non consistency and solutions](https://mlsanity.com/paper/2002.00658/) (2020)
- [The Missing Indicator Method: From Low to High Dimensions](https://mlsanity.com/paper/2211.09259/) (2022)
- [An elementary analysis of ridge regression with random design](https://mlsanity.com/paper/2203.08564/) (2022)
- [Imputation for prediction: beware of diminishing returns](https://mlsanity.com/paper/2407.19804/) (2024)
- [Random features models: a way to study the success of naive imputation](https://mlsanity.com/paper/2402.03839/) (2024)
- [Communication-Efficient Hybrid Federated Learning for E-health with Horizontal and Vertical Data Partitioning](https://mlsanity.com/paper/2404.10110/) (2024)
- [Local Risk Bounds for Statistical Aggregation](https://mlsanity.com/paper/2306.17151/) (2023)
- [Breaking the curse of dimensionality for linear rules: optimal predictors over the ellipsoid](https://mlsanity.com/paper/2509.21174/) (2025)

## Abstract (arXiv)

Training predictive models across multiple centers typically assumes that all centers collect the same set of covariates. In practice, however, they may record different features of their observations, a setting we refer to as covariate mismatch. We study linear prediction under this challenging setting, assuming center-wise MCAR missingness patterns, and develop estimators that exploit information across centers despite heterogeneous feature sets. In the low-dimensional regime, we propose a plug-in estimator of the oracle linear predictor based on component-wise aggregation of covariance and cross-moment estimates. In higher dimensions, we study an impute-then-regress strategy that first completes the missing covariates using an exchangeability-preserving imputation procedure and then fits a ridge-regularized linear model. All proposed estimators are compatible with federated learning constraints: individual-level data remain local to each center, and only aggregated quantities are exchanged. We provide asymptotic and finite-sample learning rates for our predictors, explicitly characterizing their behaviour with the global dimension, the center-specific feature partition, and the distribution of samples across centers, and validate our approach through numerical experiments.