Federated Bayesian Surveillance of Mechanical Thrombectomy Adverse Events: A Population Risk Layer for Surgical Digital Twins

Federated learning allows banks, hospitals, and other regulated organizations to train a shared model without moving raw records off their own servers, which is attractive wherever data protection law or competitive sensitivity rules out pooling data centrally. Two problems limit how far this promise can be trusted in practice. First, the parameter updates that clients exchange still leak information about local records through gradient inversion and membership inference attacks. Second, an honest averaging rule such as FedAvg has no defense against a subset of clients that submit corrupted or adversarial updates, so a small number of malicious or compromised participants can quietly steer the shared model off course. This paper presents a federated learning framework, DP-BR-FedAvg, that combines a Gaussian-mechanism differential privacy layer with a coordinate-wise trimmed-mean Byzantine-robust aggregation rule, evaluated on a simulated cross-institutional classification task resembling fraud and clinical-risk scoring. Across sixty communication rounds with twenty clients, a quarter of them Byzantine, plain FedAvg collapses on the minority class (F1-score 0.030) while the proposed framework recovers substantially more of the signal (F1-score 0.119) while bounding the privacy loss of any single client's contribution. A Byzantine-robust aggregator with no privacy layer performs best in raw accuracy, quantifying the cost privacy imposes on robustness. The results show that privacy and robustness mechanisms interact rather than simply add, and that system design for regulated, adversarial, cross-institutional settings needs to budget for that interaction.

Probabilistic certification of Bayesian neural networks lower-bounds the posterior probability that a model satisfies a verifier-defined safety property. In one-shot federated Bayesian learning, however, the deployed model is obtained by aggregating parameters drawn from client-specific posterior distributions, so local certificates do not directly guarantee safety of the aggregated model. This paper develops a deployment-consistent certification framework by propagating local posterior events through the deployment aggregation rule, with an exact geometric characterization for Federated Averaging (FedAvg). Each client constructs disjoint hyper-rectangular regions in parameter space and computes their probability masses. The server forms Cartesian products of these regions, maps them through the deployment rule, and retains a product event only when its aggregation image is verified to satisfy the safety property. Under independent client posteriors, each product-event probability factorizes into local masses, and summing verified disjoint events yields a lower bound on safety probability of the deployed model. For FedAvg with nonnegative aggregation coefficients, the image of a Cartesian product of axis-aligned hyper-rectangles is exactly a weighted hyper-rectangle, introducing no set over-approximation. We distinguish the proposed transported-event certificate from direct certification under posterior distributions induced by FedAvg and Product-of-Gaussians aggregation. Experiments on MNIST and Fashion-MNIST under label-Dirichlet heterogeneity show that the transported FedAvg certificate ranges from 22.51% to 46.89%, while direct global certificates range from 72.05% to 91.39%. Results show that predictive accuracy and certifiable safety do not necessarily follow the same trend, and that global posterior constructions can exhibit distinct certification behavior across architectures.

Conformal risk control (CRC) provides distribution-free guarantees on segmentation quality by calibrating a prediction-set threshold on held-out data. In federated deployments, the standard approach pools calibration scores across sites into a single threshold. We provide the first quantification, on real multi-institutional brain tumor data (FeTS-2022, 1,251 subjects, 20 institutions), showing that this naive pooled CRC protects the average hospital but violates coverage at 40% of individual institutions, with the worst site exceeding the target false-negative rate by 7.8 percentage points. The naive alternative, per-site local CRC, largely restores coverage but inflates prediction sets by 83x, rendering them clinically useless. We propose a shrinkage-based federated CRC protocol: each site transmits only its empirical risk curve (G scalars) to a server, which computes a shrinkage-regularized threshold per site. A single hyperparameter n0 smoothly trades worst-case coverage for prediction-set efficiency; leave-one-site-out sensitivity analysis identifies n0=19, achieving 2.7/20 violations at 2.0x stretch. We further show that direct Lagrangian optimization of coverage budgets fails, concentrating risk on vulnerable hospitals, and that the finite-sample correction term is essential: removing it triples violations. The marginal CRC guarantee is preserved by construction under the stated site-mixture assumption; per-site coverage is validated across four targets with three seeds. No patient-level images, masks, or per-volume scores leave any site.