Distributed Simultaneous Inference in Generalized Linear Models via Confidence Distribution

TL;DR

This paper introduces a distributed approach for simultaneous inference in generalized linear models that effectively combines bias-corrected estimators using confidence distributions, matching centralized data analysis performance.

Contribution

It develops a novel divide-and-combine method for regularized estimators in large datasets, with theoretical justification and practical implementation.

Findings

Achieves estimation efficiency comparable to centralized maximum likelihood estimation.

Provides nearly identical inference results as centralized analysis in simulations and real data.

Addresses uneven sub-dataset sizes with regularization techniques.

Abstract

We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N >> p, in the generalized linear models framework. When such datasets are too big to be analyzed entirely by a single centralized computer, or when datasets are already stored in distributed database systems, the strategy of divide-and-combine has been the method of choice for scalability. Due to partition, the sub-dataset sample sizes may be uneven and some possibly close to p, which calls for regularization techniques to improve numerical stability. However, there is a lack of clear theoretical justification and practical guidelines to combine results obtained from separate regularized estimators, especially when the final objective is simultaneous inference for a group of regression parameters. In this paper, we develop a strategy to combine bias-corrected lasso-type estimates by using confidence distributions. We show that the resulting combined estimator achieves the same estimation efficiency as that of the maximum likelihood estimator using the centralized data. As demonstrated by simulated and real data examples, our divide-and-combine method yields nearly identical inference as the centralized benchmark.