# Learning Centre Partitions from Summaries

arXiv: https://arxiv.org/abs/2509.16337 · HTML: https://mlsanity.com/paper/2509.16337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [Distributed Statistical Estimation and Rates of Convergence in Normal Approximation](https://mlsanity.com/paper/1704.02658/) (2017)
- [High-dimensional simultaneous inference with the bootstrap](https://mlsanity.com/paper/1606.03940/) (2016)
- [Robust Inference for Federated Meta-Learning](https://mlsanity.com/paper/2301.00718/) (2023)
- [Heterogeneity-aware Clustered Distributed Learning for Multi-source Data Analysis](https://mlsanity.com/paper/2211.02781/) (2022)

## Abstract (arXiv)

Multi-centre studies increasingly rely on distributed inference, where sites share only centre-level summaries. Homogeneity of parameters across centres is often violated, motivating methods that both test for equality and learn centre groupings before estimation. We develop multivariate Cochran-type tests that operate on summary statistics and embed them in a sequential, test-driven Clusters-of-Centres (CoC) algorithm that merges centres (or blocks) only when equality is not rejected. We derive the asymptotic chi2-mixture distributions of the test statistics and provide plug-in estimators for implementation. To improve finite-sample integration, we introduce a multi-round bootstrap CoC that re-evaluates merges across independently resampled summary sets; under mild regularity and a separation condition, we prove a golden-partition recovery result: as the number of rounds grows with n, the true partition is recovered with probability tending to one. We also give simple numerical guidelines, including a plateau-based stopping rule, to make the multi-round procedure reproducible. Simulations and a real-data analysis of U.S. airline on-time performance (2007) show accurate heterogeneity detection and partitions that change little with the choice of resampling scheme.