FedSPM: Routing-Enabled Federated Learning under Dual Heterogeneity via Semiparametric Mixture

FedSPM addresses dual heterogeneity in routing-enabled federated learning: client distributions differ across institutions, while each client may also contain latent subpopulations. It represents every client with client-specific mixture components, each combining a predictive distribution for classification with a feature distribution for routing. Feature densities are modeled through density ratios relative to a shared nonparametric measure estimated by empirical likelihood. The paper develops a federated expectation-maximization algorithm and proves an O(1/sqrt(T)) convergence rate for the exact profiled objective when surrogate errors are controlled. Experiments on controlled benchmarks and real medical data report consistent routing and prediction improvements. Code is available on GitHub.