arXiv subjects

Jonathan R. Stewart

Publications and source records attributed to Jonathan R. Stewart.

7 recordsLinked to original sources

arXiv2025

Profile monitoring of random functions with Gaussian process basis expansions

We consider the problem of online profile monitoring of random functions that admit basis expansions possessing random coefficients for the purpose of out-of-control state detection. Our approach is applicable to a broad class of random functions which feature two sources of variation: additive error and random fluctuations through random coefficients in the basis representation of functions. We focus on a two-phase monitoring problem with a first stage consisting of learning the in-control process and the second stage leveraging the learned process for out-of-control state detection. The foundations of our method are derived under the assumption that the coefficients in the basis expansion are Gaussian random variables, which facilitates the development of scalable and effective monitoring methodology for the observed processes that makes weak functional assumptions on the underlying process. We demonstrate the potential of our method through simulation studies that highlight some of the nuances that emerge in profile monitoring problems with random functions, and through an application.

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arXiv2025

Pseudo-likelihood-based $M$-estimation of random graphs with dependent edges and parameter vectors of increasing dimension

An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We demonstrate that scalable estimation of random graph models with dependent edges is possible, by establishing convergence rates of pseudo-likelihood-based $M$-estimators for discrete undirected graphical models with exponential parameterizations and parameter vectors of increasing dimension in single-observation scenarios. We highlight the impact of two complex phenomena on the convergence rate: phase transitions and model near-degeneracy. The main results have possible applications to discrete and dependent network, spatial, and temporal data. To showcase convergence rates, we introduce a novel class of generalized $β$-models with dependent edges and parameter vectors of increasing dimension, which leverage additional structure in the form of overlapping subpopulations to control dependence. We establish convergence rates of pseudo-likelihood-based $M$-estimators for generalized $β$-models in dense- and sparse-graph settings.

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arXiv2025

Consistency of empirical distributions of sequences of graph statistics in networks with dependent edges

One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number of realized events in the network, examples of which include the degree distribution, as well as the edgewise shared partner distribution, and more. We provide conditions under which the empirical distributions of sequences of graph statistics are consistent in the $\ell_{\infty}$-norm in settings where edges in the network are dependent. We accomplish this by elaborating a weak dependence condition which ensures that we can obtain exponential inequalities which bound probabilities of deviations of graph statistics from the expected value. We apply this concentration inequality to empirical distributions of sequences of graph statistics and derive non-asymptotic bounds on the $\ell_{\infty}$-error which hold with high probability. Our non-asymptotic results are then extended to demonstrate uniform convergence almost surely in selected examples. We illustrate theoretical results through examples, simulation studies, and an application.

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arXiv2025

Learning cross-layer dependence structure in multilayer networks

We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our approach separates the network formation process from the layer formation process, and is able to extend existing single-layer network models to multilayer network models that accommodate cross-layer dependence. We establish non-asymptotic and minimax-optimal error bounds for maximum likelihood estimators and demonstrate the convergence rate in scenarios of increasing parameter dimension. Additionally, we establish non-asymptotic error bounds for multivariate normal approximations and propose a model selection method that controls the false discovery rate. Simulation studies and an application to the Lazega lawyers network show that our framework and method perform well in realistic settings.

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arXiv2025

Rates of convergence and normal approximations for estimators of local dependence random graph models

Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by Schweinberger and Handcock (2015), research in the statistical network analysis and network science literatures have demonstrated the potential and utility of this class of models. In this work, we provide the first theory for estimation and inference which ensures consistent and valid inference of parameter vectors of local dependence random graph models. This is accomplished by deriving convergence rates of estimation and inference procedures for local dependence random graph models based on a single observation of the graph, allowing both the number of model parameters and the sizes of blocks to tend to infinity. First, we derive non-asymptotic bounds on the $\ell_2$-error of maximum likelihood estimators with convergence rates, outlining conditions under which these rates are minimax optimal. Second, and more importantly, we derive non-asymptotic bounds on the error of the multivariate normal approximation. These theoretical results are the first to achieve both optimal rates of convergence and non-asymptotic bounds on the error of the multivariate normal approximation for parameter vectors of local dependence random graph models.

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arXiv2024

A Latent Space Approach to Inferring Distance-Dependent Reciprocity in Directed Networks

Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modeling directed networks are severely limited by the assumption that reciprocity is homogeneous across the network. In this work, we introduce a new latent space model for directed networks that can model heterogeneous reciprocity patterns that arise from the actors' latent distances. Furthermore, existing edge-independent latent space models are nested within the proposed model class, which allows for meaningful model comparisons. We introduce a Bayesian inference procedure to infer the model parameters using Hamiltonian Monte Carlo. Lastly, we use the proposed method to infer different reciprocity patterns in an advice network among lawyers, an information-sharing network between employees at a manufacturing company, and a friendship network between high school students.

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arXiv2023

Model selection for network data based on spectral information

We introduce a new methodology for model selection in the context of modeling network data. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including stochastic block models, latent position models, and exponential families of random graph models. A persistent question in the statistical network analysis literature lies in understanding how to compare different models for the purpose of model selection and evaluating goodness-of-fit, especially when models have different mathematical foundations. In this work, we develop a novel non-parametric method for model selection in network data settings which exploits the information contained in the spectrum of the graph Laplacian in order to obtain a measure of goodness-of-fit for a defined set of network data models. We explore the performance of our proposed methodology to popular classes of network data models through numerous simulation studies, demonstrating the practical utility of our method through two applications.

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