# Network-based Neighborhood regression

arXiv: https://arxiv.org/abs/2407.04104 · HTML: https://mlsanity.com/paper/2407.04104/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [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)
- [A Review of Stochastic Block Models and Extensions for Graph Clustering](https://mlsanity.com/paper/1903.00114/) (2019)
- [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Optimal Ridge Regularization for Out-of-Distribution Prediction](https://mlsanity.com/paper/2404.01233/) (2024)
- [Covariate Regularized Community Detection in Sparse Graphs](https://mlsanity.com/paper/1607.02675/) (2016)
- [Community Detection in General Hypergraph via Graph Embedding](https://mlsanity.com/paper/2103.15035/) (2021)
- [Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing](https://mlsanity.com/paper/1811.06055/) (2018)
- [Linear regression and its inference on noisy network-linked data](https://mlsanity.com/paper/2007.00803/) (2020)
- [Mixed-Effect Time-Varying Network Model and Application in Brain Connectivity Analysis](https://mlsanity.com/paper/1806.03829/) (2018)
- [Community Detection with Dependent Connectivity](https://mlsanity.com/paper/1812.06406/) (2018)
- [Simultaneous inference for generalized linear models with unmeasured confounders](https://mlsanity.com/paper/2309.07261/) (2023)
- [Network-Adjusted Covariates for Community Detection](https://mlsanity.com/paper/2306.15616/) (2023)
- [Network assisted analysis to reveal the genetic basis of autism](https://mlsanity.com/paper/1506.00728/) (2015)

## Abstract (arXiv)

Given the ubiquity of modularity in biological systems, module-level regulation analysis is vital for understanding biological systems across various levels and their dynamics. Current statistical analysis on biological modules predominantly focuses on either detecting the functional modules in biological networks or sub-group regression on the biological features without using the network data. This paper proposes a novel network-based neighborhood regression framework whose regression functions depend on both the global community-level information and local connectivity structures among entities. An efficient community-wise least square optimization approach is developed to uncover the strength of regulation among the network modules while enabling asymptotic inference. With random graph theory, we derive non-asymptotic estimation error bounds for the proposed estimator, achieving exact minimax optimality. Unlike the root-n consistency typical in canonical linear regression, our model exhibits linear consistency in the number of nodes n, highlighting the advantage of incorporating neighborhood information. The effectiveness of the proposed framework is further supported by extensive numerical experiments. Application to whole-exome sequencing and RNA-sequencing Autism datasets demonstrates the usage of the proposed method in identifying the association between the gene modules of genetic variations and the gene modules of genomic differential expressions.