Angelo Mele, Lingxin Hao, Joshua Cape, Carey E. Priebe
arXiv 18 Aug 2019 · Statistics — Methodology · 7 citations (OpenAlex)
arXiv:1908.06438 · PDF · DOI · OpenAlex · Extracted main text
In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of covariates in stochastic blockmodels. On the theoretical side, we establish asymptotic normality of our estimators for the subsequent purpose of performing inference. On the applied side, we show that computing our estimator is much faster than standard variational expectation--maximization algorithms and scales well for large networks. Monte Carlo experiments suggest that the estimator performs well under different data generating processes. Our application to Facebook data shows evidence of homophily in gender, role and campus-residence, while allowing us to discover unobserved communities. The results in this paper provide a foundation for spectral estimation of the effect of observed covariates as well as unobserved latent community structure on the probability of link formation in networks.
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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 | Roy, Atchade \ Michailidis (2019) `Likelihood inference for large scale stochastic blockmodels with covariates based on a divide-and-conquer parallelizable algori… | 1.000 | 7 | 3 | 100% |
| 2 | Zhu \ Ghodsi (2006) `Automatic dimensionality selection from the scree plot via the use of profile likelihood.', Computational Statistics and Data A… | 1.000 | 5 | 3 | 100% |
| 3 | Athreya, Fishkind, Levin, Lyzinski, Park, Qin, Sussman, Tang, Vogels… (2018) `Statistical inference on random dot product graphs: A survey', Journal of Machine Learning Research 18(226), 1–92 | 0.971 | 12 | 6 | 92% |
| 4 | Tang \ Priebe (2018) `Limit theorems for eigenvectors of the normalized laplacian for random graphs.', Annals of Statistics 46, 2360–2415 | 0.928 | 5 | 3 | 80% |
| 5 | Bickel, Choi, Chang \ Zhang (2013) `Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels', Ann | 0.843 | 4 | 3 | 75% |
| 6 | Traud, Mucha \ A (2012) `Social structure of facebook networks', Physica A: Statistical Mechanics and its Applications 391(16), 4165–4180 | 0.843 | 4 | 3 | 75% |
| 7 | Rubin-Delanchy, Priebe, Tang \ Cape (2018) A statistical interpretation of spectral embedding: the generalised random dot product graph | 0.843 | 3 | 3 | 100% |
| 8 | Tang, Cape \ Priebe (2017) Asymptotically efficient estimators for stochastic blockmodels: The naive mle, the rank-constrained mle, and the spectral | 0.805 | 23 | 4 | 52% |
| 9 | Choi, Wolfe \ Airoldi (2011) `Stochastic blockmodels with a growing number of classes', Biometrika 99(2), 273–284 | 0.737 | 3 | 3 | 67% |
| 10 | Sweet (2015) `Incorporating covariates into stochastic blockmodels', Journal of Educational and Behavioral Statistics 40(6), 635–664 | 0.737 | 3 | 3 | 67% |
Showing the top 10 of 58 scored citations.