An Accurate and Single-Communication Federated Inference Algorithm

Joint analyses across multiple institutions are increasingly important in biomedical and epidemiological research, particularly for rare diseases where datasets are typical small. However, privacy regulations and institutional policies often prevent the sharing of individual-level patient data. In this paper we present an accurate and single-communication federated inference algorithm. Single-communication federated inference enables statistical analyses through a single exchange of summary statistics between participating centers and a coordinating server, preserving privacy while reducing communication and computational costs compared with iterative federated learning. We extend a recently proposed single-communication federated inference strategy that is based on second-order Taylor expansions by using third-order expansions to better approximate local log-likelihood functions. The proposed method is evaluated through simulation studies based on real data and compared with existing federated inference strategies. The simulation studies assess the performance of the proposed method, with a particular focus on scenarios involving small local sample sizes, where quadratic approximations may fail to capture skewness and other higher-order characteristics of the log-likelihood function. They demonstrate that incorporating higher-order information of the log-likelihood function improves the accuracy while preserving the privacy, communication efficiency, and scalability required for collaborative biomedical and epidemiological research.

Generation-Powered Inference for Distribution-Valued Outcomes

Modern generative models increasingly produce distribution-valued outputs, such as predicted cellular responses to genetic perturbations in single-cell genomics. While these models provide valuable auxiliary information, they are inherently imperfect, creating a need for statistical methods that leverage their predictions without relying on their correctness. We propose generation-powered inference (GPI), a general framework for improving inference on distribution-valued parameters using auxiliary generative models. Focusing on Wasserstein barycenters and related distributional functionals, we introduce a function-valued bridge representation that transforms inference in the nonlinear Wasserstein space into estimation of a mean function in a Hilbert space, enabling an augmented estimation framework analogous to prediction-powered inference. We develop a family of GPI estimators with optimal information borrowing, establish consistency, asymptotic normality, and simultaneous confidence bands, and derive valid inference for linear functionals and Wasserstein distances. Simulation studies demonstrate efficiency gains over labeled-data-only methods and robust performance under generative model misspecification. We illustrate the proposed framework using a Perturb-seq study of K562 cells, where synthetic perturbation responses generated by the State foundation model are used to improve inference for pathway-level consensus gene expression distributions associated with perturbations of the 40S ribosome module.