We show that a simple community detection algorithm originated from stochastic blockmodel literature achieves consistency, and even optimality, for a broad and flexible class of sparse latent space models. The class of models includes latent eigenmodels (Hoff, 2008). The community detection algorithm is based on spectral clustering followed by local refinement via normalized edge counting. It is easy to implement and attains high accuracy with a low computational budget. The proof of its optimality depends on a neat equivalence between likelihood ratio test and edge counting in a simple vs. simple hypothesis testing problem that underpins the refinement step, which could be of independent interest.

Latent space models are effective tools for statistical modeling and visualization of network data. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing the likelihood function for an existing class of inner-product models, and we establish their statistical rates of convergence for these models. In addition, the theory informs us that both methods work simultaneously for a wide range of different latent space models that allow latent positions to affect edge formation in flexible ways, such as distance models. Furthermore, the effectiveness of the methods is demonstrated on a number of real world network data sets for different statistical tasks, including community detection with and without edge covariates, and network assisted learning.

Motivated by the need to predict the future biometric performance of the U.S. Visitor and Immigrant Status Indicator Technology program as it increases the size of its watchlist database, we use extreme-value theory (which is an asymptotic theory for the maximum of a large number of independent and identically distributed random variables) to analyze biometric performance as the gallery size gets very large. Due to the lack of published data for open-set fingerprint systems (where some users of the system are not on the watchlist), we assess the accuracy of our approach using the rank-one identification probability for closed-set fingerprint systems (where all users are on the watchlist). Consistent with earlier empirical observations, we find that the relationship between the rank-one identification probability and gallery size is log-linear to first-order and has a quadratic correction term, at least under our specific distributional assumptions. We also find that the probabilistic biometric model provides a good fit to empirical fingerprint data only when the genuine and impostor similarity scores are allowed to depend on the quality of the fingerprint images, which leads to genuine and impostor scores that are mixtures of distributions. Finally, we use the extreme-value approach to derive the receiver operating characteristic curve for open-set systems.