Statistical Inference on Random Dot Product Graphs: a Survey
By Avanti Athreya, Donniell E. Fishkind, Minh Tang, Carey E. Priebe, Youngser Park, Joshua T. Vogelstein, Keith D. Levin, Vince Lyzinski, Yichen Qin, Daniel Lewis Sussman. 2017
290 citations recorded by the source corpus.
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describe a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices. We examine the analogues, in graph inference, of several canonical tenets of classical Euclidean inference: in particular, we summarize a body of existing results on the consistency and asymptotic normality of the adjacency and Laplacian spectral embeddings, and the role these spectral embeddings can play in the construction of single- and multi-sample hypothesis tests for graph data. We investigate several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome. We outline requisite background and current open problems in spectral graph inference.
Subfields: Artificial Intelligence, Statistics and Probability, Graph Learning
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Hayden S. Helm
- Carey E. Priebe
- Oriana Riva
- Ali Geisa
- Christopher M. White
- Weiwei Yang
- Sujeeth Bharadwaj
- Kate Lytvynets
In Statistics and Probability
In Graph Learning
Citations in the corpus
- Asymptotically perfect seeded graph matching without edge correlation (and applications to inference) (2025, unknown): “Our analysis will be couched within the context of Random Dot Product Graphs (RDPG) of [30], a class of latent position graph models [31] that are particularly amenable to subsequent analysis [29].”
- Convergence Guarantees for Response Prediction for Latent Structure Network Time Series (2025, unknown): “Each time series represents a multilayer network on a common set of nodes, and raw stress embedding, a popular dimensionality reduction tool, is used for capturing the unknown latent low dimensional structure.”
- Inducing a hierarchy for multi-class classification problems (2021, methodology): “Embedding methods such as multi-dimensional scaling (Wickelmaier, 2003) and spectral embedding (Von Luxburg, 2007) are well studied in particular settings (Dokmanic et al., 2015; Athreya et al., 2017) and are generally used as dimensionality reduction techniques for clustering (Lyzinski et al.”