Federated Likelihood-based Inference via Sobolev Neural Approximation

Thomas M. Menino Convention & Exhibition Center 

Statistical inference is increasingly performed in federated environments where individual-level data cannot be pooled. However, practical deployment is often constrained by communication costs that make iterative exchange of summary statistics logistically prohibitive. One-shot federated inference, which requires only a single round of communication, is therefore highly desirable but remains challenging in the presence of distributional heterogeneity, or high-dimensional parameters. To address these challenges, we propose a one-shot federated inference framework that reconstructs the pooled likelihood function by aggregating function approximations of site-specific likelihoods. We use neural networks to approximate local likelihood functions and impose Sobolev-norm regularization to jointly control approximation error in both likelihood values and gradients. We establish theoretical results showing how functional approximation error propagates to estimation error of the resulting federated estimator. We demonstrate its effectiveness through likelihood-based inference for logistic regression and stratified Cox models, with an application to a multi-site EHR study.

One-shot Federated Inference

Function Approximation

Sobolev Training 

Section on Statistical Learning and Data Science