arXiv subjects

Carey E Priebe

Publications and source records attributed to Carey E Priebe.

4 recordsLinked to original sources

arXiv2026

Vertex misalignment and changepoint localization in network time series

Inference for time series of networks often relies on accurate vertex correspondence between network realizations at different times. In practice, however, such vertex alignments can be misspecified or unknown. We study the impact of vertex alignment on changepoint localization for dynamic networks through two illustrative models, each with a similar changepoint, with the key distinction being whether changepoint information is contained in marginal or joint distributions of the time-varying latent positions. We compare localization techniques ranging from the simple network statistic of average degree to the modern procedure of Euclidean mirrors. In one model, vertex misalignment causes little error, and in the other, it impairs localization in ways that cannot be corrected through graph matching or optimal transport, which we show are closely related in this setting. Our results demonstrate that robust network inference necessitates reckoning with the subtle interplay of marginal and joint information in the observed network time series.

math.ST↗

arXiv2024

Euclidean mirrors and dynamics in network time series

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations, called Euclidean mirrors, permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.

stat.ME↗

arXiv2019

Central Limit Theorems for Classical Multidimensional Scaling

Classical multidimensional scaling is a widely used method in dimensionality reduction and manifold learning. The method takes in a dissimilarity matrix and outputs a low-dimensional configuration matrix based on a spectral decomposition. In this paper, we present three noise models and analyze the resulting configuration matrices, or embeddings. In particular, we show that under each of the three noise models the resulting embedding gives rise to a central limit theorem. We also provide compelling simulations and real data illustrations of these central limit theorems. This perturbation analysis represents a significant advancement over previous results regarding classical multidimensional scaling behavior under randomness.

stat.ME↗

arXiv2013

On latent position inference from doubly stochastic messaging activities

We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent positions from a stream of messaging activity data. Each of the message-exchanging actors is modeled as a process in a latent space. The actors' latent positions are assumed to be influenced by the distribution of a much larger population over the latent space. Each actor's movement in the latent space is modeled as being governed by two parameters that we call confidence and visibility, in addition to dependence on the population distribution. The messaging frequency between a pair of actors is assumed to be inversely proportional to the distance between their latent positions. Our inference algorithm is based on a projection approach to an online filtering problem. The algorithm associates each actor with a probability density-valued process, and each probability density is assumed to be a mixture of basis functions. For efficient numerical experiments, we further develop our algorithm for the case where the basis functions are obtained by translating and scaling a standard Gaussian density.

stat.ML↗