Vertex nomination, consistent estimation, and adversarial modification

Agterberg, Joshua; Park, Youngser; Larson, Jonathan; White, Christopher M.; Priebe, Carey E.; Lyzinski, Vince

doi:10.1214/20-ejs1744

Cited by 12 publications

(12 citation statements)

References 43 publications

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“…Recently proposed methods for vertex nomination [3,[17][18][19][20][21][22] have been quite successful in a variety of settings when the definition of similar is defined explicitly by a domain expert. Approaches are mainly combinatorial or spectral.…”

Section: Vertex Nominationmentioning

confidence: 99%

Leveraging semantically similar queries for ranking via combining representations

Helm¹,

Abdin²,

Pedigo³

et al. 2021

Preprint

Self Cite

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In modern ranking problems, different and disparate representations of the items to be ranked are often available. It is sensible, then, to try to combine these representations to improve ranking. Indeed, learning to rank via combining representations is both principled and practical for learning a ranking function for a particular query. In extremely data-scarce settings, however, the amount of labeled data available for a particular query can lead to a highly variable and ineffective ranking function. One way to mitigate the effect of the small amount of data is to leverage information from semantically similar queries. Indeed, as we demonstrate in simulation settings and real data examples, when semantically similar queries are available it is possible to gainfully use them when ranking with respect to a particular query. We describe and explore this phenomenon in the context of the bias-variance trade off and apply it to the data-scarce settings of a Bing navigational graph and the Drosophila larva connectome.

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Section: Vertex Nominationmentioning

confidence: 99%

Leveraging semantically similar queries for ranking via combining representations

Helm¹,

Abdin²,

Pedigo³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…These hypothesis arise naturally in many applications, including vertex nomination (Fishkind et al, 2015) and role discovery (Gilpin et al, 2013); in both of these applications we are given a graph G together with a notion of "interesting" vertices and our task is to find vertices in G that are most "interesting". Examples include finding outliers in a stochastic block model with adversarial outliers nodes (Agterberg et al, 2020;Cai and Li, 2015) or finding vertices that are most "similar" to a given subset of vertices. Testing for equality of latent positions is also useful as a post-processing step for two-sample testing problems on graphs.…”

Section: Introductionmentioning

confidence: 99%

Hypothesis Testing for Equality of Latent Positions in Random Graphs

Du¹,

Tang²

2021

Preprint

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We consider the hypothesis testing problem that two vertices i and j of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special cases of this hypotheses test include testing whether two vertices in a stochastic block model or degree-corrected stochastic block model graph have the same block membership vectors. We propose several test statistics based on the empirical Mahalanobis distances between the ith and jth rows of either the adjacency or the normalized Laplacian spectral embedding of the graph. We show that, under mild conditions, these test statistics have limiting chi-square distributions under both the null and local alternative hypothesis, and we derived explicit expressions for the non-centrality parameters under the local alternative. Using these limit results, we address the model selection problem of choosing between the standard stochastic block model and its degree-corrected variant. The effectiveness of our proposed tests are illustrated via both simulation studies and real data applications.

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“…Furthermore, asymptotic normality results exist for the ASE [7] and LSE [36]. In addition to these theoretical results, these spectral techniques have been applied to graph machine learning, including vertex nomination [42,3], vertex embedding and classification [35,12], and joint embedding [39] problems.…”

mentioning

confidence: 99%

Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming

Wu¹,

Palmer²,

DeFord³

2021

Preprint

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We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.

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Vertex nomination, consistent estimation, and adversarial modification

Cited by 12 publications

References 43 publications

Leveraging semantically similar queries for ranking via combining representations

Leveraging semantically similar queries for ranking via combining representations

Hypothesis Testing for Equality of Latent Positions in Random Graphs

Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming

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