# Heterogeneity-aware and communication-efficient distributed statistical inference

arXiv: https://arxiv.org/abs/1912.09623 · HTML: https://mlsanity.com/paper/1912.09623/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 15 of 15)

- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach](https://mlsanity.com/paper/2108.12112/) (2021)
- [Federated Offline Reinforcement Learning](https://mlsanity.com/paper/2206.05581/) (2022)
- [Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling](https://mlsanity.com/paper/2111.14008/) (2021)
- [Multi-Task Learning with Summary Statistics](https://mlsanity.com/paper/2307.02388/) (2023)
- [Heterogeneous Federated Learning on a Graph](https://mlsanity.com/paper/2209.08737/) (2022)
- [Late Fusion Multi-task Learning for Semiparametric Inference with Nuisance Parameters](https://mlsanity.com/paper/2507.07941/) (2025)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [Heterogeneous Transfer Learning for Building High-Dimensional Generalized Linear Models with Disparate Datasets](https://mlsanity.com/paper/2312.12786/) (2023)
- [MANDERA: Malicious Node Detection in Federated Learning via Ranking](https://mlsanity.com/paper/2110.11736/) (2021)
- [Distributed Estimation and Inference for Semi-parametric Binary Response Models](https://mlsanity.com/paper/2210.08393/) (2022)
- [Distributed Linear Regression with Compositional Covariates](https://mlsanity.com/paper/2310.13969/) (2023)
- [Bayesian Federated Inference for regression models based on non-shared multicenter data sets from heterogeneous populations](https://mlsanity.com/paper/2402.02898/) (2024)
- [Hierarchical Projection for Adaptive Knowledge Transfer](https://mlsanity.com/paper/2606.08691/) (2026)
- [Renewable Lasso without Batch-Number Constraints: A Gradient-Enhanced Approach](https://mlsanity.com/paper/2606.11738/) (2026)

## Abstract (arXiv)

In multicenter research, individual-level data are often protected against sharing across sites. To overcome the barrier of data sharing, many distributed algorithms, which only require sharing aggregated information, have been developed. The existing distributed algorithms usually assume the data are homogeneously distributed across sites. This assumption ignores the important fact that the data collected at different sites may come from various sub-populations and environments, which can lead to heterogeneity in the distribution of the data. Ignoring the heterogeneity may lead to erroneous statistical inference. In this paper, we propose distributed algorithms which account for the heterogeneous distributions by allowing site-specific nuisance parameters. The proposed methods extend the surrogate likelihood approach to the heterogeneous setting by applying a novel density ratio tilting method to the efficient score function. The proposed algorithms maintain the same communication cost as the existing communication-efficient algorithms. We establish a non-asymptotic risk bound for the proposed distributed estimator and its limiting distribution in the two-index asymptotic setting which allows both sample size per site and the number of sites to go to infinity. In addition, we show that the asymptotic variance of the estimator attains the Cram'er-Rao lower bound when the number of sites is in rate smaller than the sample size at each site. Finally, we use simulation studies and a real data application to demonstrate the validity and feasibility of the proposed methods.