# Subsampling bootstrap of count features of networks

arXiv: https://arxiv.org/abs/1312.2645 · HTML: https://mlsanity.com/paper/1312.2645/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2013.

## Built on by (most cited first, 8 of 8)

- [One-Hot Graph Encoder Embedding](https://mlsanity.com/paper/2109.13098/) (2021)
- [Estimating Graph Dimension with Cross-validated Eigenvalues](https://mlsanity.com/paper/2108.03336/) (2021)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Higher-order accurate two-sample network inference and network hashing](https://mlsanity.com/paper/2208.07573/) (2022)
- [Confidence Intervals for Error Rates in 1:1 Matching Tasks: Critical Statistical Analysis and Recommendations](https://mlsanity.com/paper/2306.01198/) (2023)
- [Block Dense Weighted Networks with Augmented Degree Correction](https://mlsanity.com/paper/2105.12290/) (2021)
- [Stochastic Step-wise Feature Selection for Exponential Random Graph Models (ERGMs)](https://mlsanity.com/paper/2307.12862/) (2023)
- [Valid Bootstraps for Network Embeddings with Applications to Network Visualisation](https://mlsanity.com/paper/2410.20895/) (2024)

## Abstract (arXiv)

Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or ``moments'' (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280-2301]) and smooth functions of these features for the networks. Using these methods, we cannot only estimate the variance of count features but also get good estimates of such feature counts, which are usually expensive to compute numerically in large networks. In our paper, we prove theoretical properties of the bootstrap estimates of variance of the count features as well as show their efficacy through simulation. We also use the method on some real network data for estimation of variance and expectation of some count features.