# Shapley Value Estimation for Multi-Site Data with Blockwise-Missing Features

arXiv: https://arxiv.org/abs/2609.14902 · HTML: https://mlsanity.com/paper/2609.14902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Improving KernelSHAP: Practical Shapley Value Estimation via Linear Regression](https://mlsanity.com/paper/2012.01536/) (2020)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [A Perspective on Explainable Artificial Intelligence Methods: SHAP and LIME](https://mlsanity.com/paper/2305.02012/) (2023)
- [Secure Shapley Value for Cross-Silo Federated Learning (Technical Report)](https://mlsanity.com/paper/2209.04856/) (2022)
- [Integrating multi-source block-wise missing data in model selection](https://mlsanity.com/paper/1901.03797/) (2019)
- [Explaining medical AI performance disparities across sites with confounder Shapley value analysis](https://mlsanity.com/paper/2111.08168/) (2021)
- [Modular Regression: Improving Linear Models by Incorporating Auxiliary Data](https://mlsanity.com/paper/2211.10032/) (2022)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximation](https://mlsanity.com/paper/2505.08198/) (2025)
- [Efficient Semiparametric Inference for Distributed Data with Blockwise Missingness](https://mlsanity.com/paper/2508.16902/) (2025)
- [Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR](https://mlsanity.com/paper/2602.06713/) (2026)
- [Distributionally Robust Transfer Learning with Structurally Missing Covariates, with Application to Cross-National Cardiac Arrest Prediction](https://mlsanity.com/paper/2605.24212/) (2026)

## Abstract (arXiv)

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 FUSHAP (Fusion Shapley Attribution from Partially-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× lower MSE than the single-site estimator and 2--3× 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× relative to the single-site estimator; in the clinical application, standard imputation can increase MSE above the single-site baseline.