Federated Shapley Values

The core mechanism relies on computing the marginal contribution of a feature by comparing model predictions with and without that feature. In a federated context, this requires a secure aggregation protocol to sum the differences in model output across all data partitions without revealing any single institution's raw predictions. The global Shapley value is the weighted average of these contributions, computed entirely on encrypted or locally aggregated statistics.

Direct computation of exact Shapley values is combinatorially expensive. Federated systems often train a surrogate explainer model (e.g., KernelSHAP) on a public or synthetically generated dataset. The global model's predictions on this surrogate dataset are queried by each client, and the local loss functions for the explainer are aggregated via Federated Averaging (FedAvg) to produce a global explanation model without accessing private data.

A critical challenge arises when feature distributions vary significantly across institutions (non-IID data). A feature's global Shapley value may obscure local heterogeneity. Advanced implementations compute personalized federated Shapley values by clustering clients with similar feature attributions or by decomposing the global value into a shared component and a local offset, providing both a network-wide view and site-specific interpretability.

For regulatory compliance, the computation of Shapley values must be auditable. Federated systems integrate cryptographic commitments and zero-knowledge proofs to verify that each institution correctly computed its local marginal contributions according to the agreed-upon protocol. This creates an immutable, verifiable log of the entire explanation process without revealing the underlying patient data used in the computation.

To reduce the bandwidth overhead of computing explanations across many clients, federated Shapley value algorithms employ stratified sampling of feature coalitions. Instead of transmitting updates for every possible feature subset, clients only compute contributions for a carefully selected, synchronized subset of coalitions. Gradient compression techniques are then applied to the explanation updates to further minimize communication costs.

The Shapley value computation itself can leak information about the training data. To provide a formal privacy guarantee, calibrated Gaussian noise is added to the aggregated feature attributions before they are released. The privacy budget (epsilon) consumed by this explanation query is tracked alongside the training budget, ensuring the total privacy loss remains within acceptable bounds defined by the institution's governance policies.