# SIMPLE-RC: Group Network Inference with Non-Sharp Nulls and Weak Signals

arXiv: https://arxiv.org/abs/2211.00128 · HTML: https://mlsanity.com/paper/2211.00128/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Limit theorems for eigenvectors of the normalized Laplacian for random graphs](https://mlsanity.com/paper/1607.08601/) (2016)
- [Optimal hypothesis testing for stochastic block models with growing degrees](https://mlsanity.com/paper/1705.05305/) (2017)
- [Estimating the number of communities in networks by spectral methods](https://mlsanity.com/paper/1507.00827/) (2015)
- [Testing for Global Network Structure Using Small Subgraph Statistics](https://mlsanity.com/paper/1710.00862/) (2017)
- [Optimal Adaptivity of Signed-Polygon Statistics for Network Testing](https://mlsanity.com/paper/1904.09532/) (2019)
- [Recovering shared structure from multiple networks with unknown edge distributions](https://mlsanity.com/paper/1906.07265/) (2019)
- [SIMPLE: Statistical Inference on Membership Profiles in Large Networks](https://mlsanity.com/paper/1910.01734/) (2019)
- [Network resampling for estimating uncertainty](https://mlsanity.com/paper/2206.13088/) (2022)

## Built on by (most cited first, 1 of 1)

- [Inferences on Mixing Probabilities and Ranking in Mixed-Membership Models](https://mlsanity.com/paper/2308.14988/) (2023)

## Abstract (arXiv)

Large-scale network inference with uncertainty quantification has important applications in natural, social, and medical sciences. The recent work of Fan, Fan, Han and Lv (2022) introduced a general framework of statistical inference on membership profiles in large networks (SIMPLE) for testing the sharp null hypothesis that a pair of given nodes share the same membership profiles. In real applications, there are often groups of nodes under investigation that may share similar membership profiles at the presence of relatively weaker signals than the setting considered in SIMPLE. To address these practical challenges, in this paper we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the non-sharp null hypothesis that a group of given nodes share similar (not necessarily identical) membership profiles under weaker signals. Utilizing the idea of random coupling, we construct our test as the maximum of the SIMPLE tests for subsampled node pairs from the group. Such technique reduces significantly the correlation among individual SIMPLE tests while largely maintaining the power, enabling delicate analysis on the asymptotic distributions of the SIMPLE-RC test. Our method and theory cover both the cases with and without node degree heterogeneity. These new theoretical developments are empowered by a second-order expansion of spiked eigenvectors under the ℓ_∞-norm, built upon our work for random matrices with weak spikes. Our theoretical results and the practical advantages of the newly suggested method are demonstrated through several simulation and real data examples.