# Network Cluster-Robust Inference

arXiv: https://arxiv.org/abs/2103.01470 · HTML: https://mlsanity.com/paper/2103.01470/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2402.01845/) (2024)
- [Online Experimental Design With Estimation-Regret Trade-off Under Network Interference](https://mlsanity.com/paper/2412.03727/) (2024)
- [Graph-Dependent Regret Bounds in Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2503.07555/) (2025)
- [Clustered Switchback Designs for Experimentation Under Spatio-temporal Interference](https://mlsanity.com/paper/2312.15574/) (2023)
- [Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference](https://mlsanity.com/paper/2510.07646/) (2025)
- [The Condition-Number Principle for Prototype Clustering](https://mlsanity.com/paper/2604.07744/) (2026)

## Abstract (arXiv)

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster-robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network-dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster-robust methods control size better than HAC estimators. However, for important classes of networks lacking low-conductance clusters, the former can exhibit substantial size distortion. To determine the number of low-conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low-conductance clusters and spectral clustering to construct them.