arXiv 26 Feb 2024 · Econometrics
arXiv:2402.16322 · PDF · DOI · OpenAlex · Extracted main text
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible framework in which each edge probability, together with the probability of community assignment, are also impacted by observed covariates. We propose a computationally tractable two-step procedure to estimate the conditional edge probabilities as well as the community assignment probabilities. The first step relies on a spectral clustering algorithm applied to a localized adjacency matrix of the network. In the second step, k-nearest neighbor regression estimates are computed on the extracted communities. We study the statistical properties of these estimators by providing non-asymptotic bounds.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Rohe, Qin, and Yu (2016) Co-clustering directed graphs to discover asymmetries and directional communities | 1.000 | 8 | 3 | 100% |
| 2 | Lei and Rinaldo (2015) Consistency of spectral clustering in stochastic block models | 1.000 | 7 | 3 | 100% |
| 3 | Jiang (2019) Non-asymptotic uniform rates of consistency for k-nn regression | 0.874 | 7 | 2 | 100% |
| 4 | Vershynin (2018) High-dimensional probability: An introduction with applications in data science | 0.811 | 4 | 2 | 100% |
| 5 | Portier (2021) Nearest neighbor process: weak convergence and non-asymptotic bound | 0.659 | 7 | 2 | 43% |
| 6 | Vu and Lei (2013) Minimax sparse principal subspace estimation in high dimensions | 0.585 | 3 | 1 | 100% |
| 7 | Bhatia (2013) Matrix analysis | 0.405 | 1 | 1 | 100% |
| 8 | Bickel, Chen, and Levina (2011) The method of moments and degree distributions for network models | 0.405 | 1 | 1 | 100% |
| 9 | Chung and Lu (2006) Complex graphs and networks | 0.405 | 1 | 1 | 100% |
| 10 | Horn and Johnson (1990) Matrix Analysis | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Flexible Imputation of Incomplete Network Data | 0.405 | 1 | 1 |
| 2 | Post-selection inference for network structure 1 | 0.405 | 1 | 1 |