Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features
Abstract
Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves $3−−8\times$ lower MSE than the single-site estimator and $2−−3\times$ lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with 82% power at moderate misalignment and 100% for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately $3−−7\times$ relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.
Related
- Global synchronization for multi-source data integration under blockwise missing patterns
- BRACE: Blockwise Rank Aggregation for Correlation Estimation
- High-dimensional reliability-oriented Shapley effects estimation
- Bayesian nonparametric inference for modal missing species and features
- SENECA: Small-Sample Discrete Entropy Estimation via Self-Consistent Missing Mass
BibTeX
@misc{li2026shapley,
title = {{Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features}},
author = {Siqi Li and Wangxuan Fan and Yiming Li and Doudou Zhou and Molei Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14902},
eprint = {2609.14902},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14902},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features
AU - Siqi Li
AU - Wangxuan Fan
AU - Yiming Li
AU - Doudou Zhou
AU - Molei Liu
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14902
UR - https://arxiv.org/abs/2609.14902
AB - Shapley value (SV)-based methods are the prevailing framework for feature attribution in machine learning, yet existing population-level Shapley estimators generally assume that observations used to evaluate the coalitional game are fully observed under a common feature space. This assumption is routinely violated in multi-site studies across biomedicine, social science, and environmental monitoring, where institutions record different features under different protocols, producing systematic blockwise missingness across sources. We first show that the standard remedy of imputing missing features before computing Shapley values introduces systematic, coalition-dependent bias into the resulting attributions. We then propose \textbf{FUSHAP} (\textbf{Fu}sion \textbf{Sh}apley \textbf{A}ttribution from \textbf{P}artially-observed data), a method that leverages partially-observed auxiliary sites to reduce the variance of a preliminary single-site Shapley estimate without imputation. A permutation-based screening step detects and excludes sites whose data distributions are incompatible with the target population. In synthetic experiments, FUSHAP achieves $3−−8\times$ lower MSE than the single-site estimator and $2−−3\times$ lower MSE than imputation baselines without incurring imputation-induced bias, and the screening procedure identifies misaligned sites with 82% power at moderate misalignment and 100% for strong misalignment. On multi-site air quality and multi-center clinical data, FUSHAP reduces MSE by approximately $3−−7\times$ relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.
ER -