High-Dimensional Assisted Learning for Vertically Distributed Data with Blockwise Missingness

2026-08-17

AI Summary

This study addresses high-dimensional sparse estimation under dual feature and response missingness in multi-institutional vertical federated learning by proposing ALB, a serverless collaborative framework. Leveraging regularized available-case loss with cyclic block coordinate updates, sample-level linear summaries, and privacy perturbation, ALB enables √n-rate asymptotically normal inference and error decomposition without data pooling. Communication complexity depends solely on sample size and exhibits geometric convergence. Empirically, ALB approaches centralized benchmarks and outperforms complete-case Lasso, with effectiveness validated on multimodal Alzheimer’s disease data. These results establish a new paradigm for privacy-preserving high-dimensional statistical inference in distributed settings with incomplete data.

Abstract

In multi-institutional studies, different parties hold distinct feature blocks for partially overlapping sets of individuals. Responses may also be missing for some records. In such settings, we propose Assisted Learning with Block-Missing Data (ALB) for sparse high-dimensional linear estimation and coordinatewise inference without pooling records or relying on a coordinating server. ALB minimizes a regularized available-case quadratic loss using cyclic block updates. Each cycle communicates $O(n)$ scalars through sample-level linear summaries, regardless of data dimension $p$, and the iterates converge geometrically to the centralized solution. We derive estimation rates that separate statistical and optimization errors. For inference on a target coefficient, ALB estimates the corresponding precision column and uses a sample-level variance estimator that accounts for dependence among moments computed from overlapping samples. Under sparsity and overlap conditions, the studentized estimator is asymptotically standard normal at the $\sqrt n$ rate, even when there are no complete cases. We also study one-time perturbed covariate and response releases that reduce direct disclosure by replacing unperturbed sample-level quantities with noisy versions. Simulations and an analysis of multimodal Alzheimer's Disease Neuroimaging Initiative data indicate that ALB approximates its centralized benchmark and improves upon complete-case Lasso by incorporating partially observed records.

Problem

• Vertically Distributed Data
• Blockwise Missingness
• High-Dimensional Linear Estimation
• Coordinatewise Inference
• Multi-institutional Studies

Innovation

• Assisted Learning
• Blockwise Missingness
• Vertically Distributed Data
• High-Dimensional Inference
• Privacy-Preserving Communication