arXiv subjects

Michael Schweinberger

Publications and source records attributed to Michael Schweinberger.

At least 19 recordsLinked to original sources

arXiv2026

Causal inference in connected populations with contagion

We address a gap in the literature on causal inference in connected populations: while there is a growing body of work on estimating causal effects in connected populations, little is known about how contagion and other network processes impact causal effects and inference. Contagion and other network processes imply that the outcomes of units affect the outcomes of other units, which enables the effects of interventions to propagate throughout connected populations and complicates insight into causal effects and inference. We offer novel insight into how contagion and other network processes impact causal effects and inference based on closed-form expressions for causal effects under spillover and contagion. These closed-form expressions reveal that the main effects of interventions, spillover, and contagion are intertwined even in the simplest possible settings, and that contagion can decrease or increase causal effects. We discuss statistical implications, including asymptotic bias of model-based estimators ignoring contagion, the violation of neighborhood exposure assumptions by unrestricted contagion and its effect on design-based estimators, and possible remedies.

stat.ME↗

arXiv2026

Causal Inference Under Network Interference

We review recent advances in causal inference under interference, drawing on a complex and diverse body of work ranging from causal inference, network science, the health sciences, economics, and the social sciences. Interference in connected populations implies that the treatment assignments of units can affect the outcomes of other units directly (via spillover) and indirectly (via contagion). Examples include public health interventions, economic and financial interventions, and advertising on social media. We review tests for detecting interference, causal effects based on fixed and random potential outcomes, identification of causal effects, and design- and model-based estimators of causal effects based on experimental and observational data. We then discuss the scope of causal conclusions based on fixed and random potential outcomes and interference graphs. Using simulations, we demonstrate that conditioning on interference graphs limits causal conclusions when the variability across interference graphs is high. We conclude with a selection of open problems.

stat.ME↗

arXiv2026

R Package iglm: Regression under Interference in Connected Populations

We introduce R package iglm, which implements a comprehensive framework for studying relationships among predictors and outcomes under interference. The implemented regression framework facilitates the study of spillover and other phenomena in connected populations and has important advantages over existing packages, among them scalability and provable theoretical guarantees. On the computational side, the regression framework relies on scalable methods that can be applied to small and large data sets, by solving a convex optimization program based on pseudo-likelihoods using Minorization-Maximization and Quasi-Newton algorithms. On the statistical side, the regression framework comes with provable theoretical guarantees. To increase the versatility of iglm, users can add custom-built model terms. We showcase iglm using two data sets, including hate speech on the social media platform X and communications among students.

stat.CO↗

arXiv2026

Scalable Sample-to-Population Estimation of Hyperbolic Space Models for Hypergraphs

Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are purchased together. Despite the vast range of applications, the statistical analysis of hypergraphs is challenging: There are many hyperedges of small and large sizes, and hyperedges can overlap or be nested. Existing approaches to hypergraphs are either not scalable or achieve scalability at the expense of model realism. We develop a statistical framework that enables scalable estimation, simulation, and model assessment of hypergraph models, which is supported by non-asymptotic and asymptotic theoretical guarantees. First, we introduce a novel model of hypergraphs capturing core-periphery structure in addition to proximity, by embedding units in an unobserved hyperbolic space. Second, we achieve scalability by developing manifold optimization algorithms for learning hyperbolic space models based on samples from a population hypergraph. Third, we provide non-asymptotic and asymptotic theoretical guarantees for learning hyperbolic space models based on samples from a population hypergraph. We use the proposed statistical framework to detect core-periphery structure along with proximity among U.S.\ politicians based on historical media reports.

stat.ME↗

arXiv2025

Vulnerability Webs: Systemic Risk in Software Networks

Software development relies on code reuse to minimize costs, creating vulnerability risks through dependencies with substantial economic impact, as seen in the Crowdstrike and HeartBleed incidents. We analyze 52,897 dependencies across 16,102 Python repositories using a strategic network formation model incorporating observable and unobservable heterogeneity. Through variational approximation of conditional distributions, we demonstrate that dependency creation generates negative externalities. Vulnerability propagation, modeled as a contagion process, shows that popular protection heuristics are ineffective. AI-assisted coding, on the other hand, offers an effective alternative by enabling dependency replacement with in-house code.

econ.EM↗

arXiv2025

A regression framework for studying relationships among attributes under network interference

To understand how the interconnected and interdependent world of the twenty-first century operates and make model-based predictions, joint probability models for networks and interdependent outcomes are needed. We propose a comprehensive regression framework for networks and interdependent outcomes with multiple advantages, including interpretability, scalability, and provable theoretical guarantees. The regression framework can be used for studying relationships among attributes of connected units and captures complex dependencies among connections and attributes, while retaining the virtues of linear regression, logistic regression, and other regression models by being interpretable and widely applicable. On the computational side, we show that the regression framework is amenable to scalable statistical computing based on convex optimization of pseudo-likelihoods using minorization-maximization methods. On the theoretical side, we establish convergence rates for pseudo-likelihood estimators based on a single observation of dependent connections and attributes. We demonstrate the regression framework using simulations and an application to hate speech on the social media platform X.

stat.ME↗

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.

math.ST↗

arXiv2024

A Continuous-Time Stochastic Process for High-Resolution Network Data in Sports

Technological advances have paved the way for collecting high-resolution network data in basketball, football, and other team-based sports. Such data consist of interactions among players of competing teams indexed by space and time. High-resolution network data are vital to understanding and predicting the performance of teams, because the performance of a team is more than the sum of the strengths of its individual players: Whether a collection of players forms a strong team depends on the strength of the individual players as well as the interactions among the players. We introduce a continuous-time stochastic process as a model of interactions among players of competing teams indexed by space and time, discuss basic properties of the continuous-time stochastic process, and learn the stochastic process from high-resolution network data by pursuing a Bayesian approach. We present simulation results along with an application to Juventus Turin, Inter Milan, and other football clubs in the premier Italian soccer league.

stat.AP↗

arXiv2023

A latent process model for monitoring progress towards hard-to-measure targets, with applications to mental health and online educational assessments

The recent shift to remote learning and work has aggravated long-standing problems, such as the problem of monitoring the mental health of individuals and the progress of students towards learning targets. We introduce a novel latent process model with a view to monitoring the progress of individuals towards a hard-to-measure target of interest, measured by a set of variables. The latent process model is based on the idea of embedding both individuals and variables measuring progress towards the target of interest in a shared metric space, interpreted as an interaction map that captures interactions between individuals and variables. The fact that individuals are embedded in the same metric space as the target helps assess the progress of individuals towards the target. We demonstrate, with the help of simulations and applications, that the latent process model enables a novel look at mental health and online educational assessments in disadvantaged subpopulations.

stat.AP↗

arXiv2023

A Socio-Demographic Latent Space Approach to Spatial Data When Geography is Important but Not All-Important

Many models for spatial and spatio-temporal data assume that "near things are more related than distant things," which is known as the first law of geography. While geography may be important, it may not be all-important, for at least two reasons. First, technology helps bridge distance, so that regions separated by large distances may be more similar than would be expected based on geographical distance. Second, geographical, political, and social divisions can make neighboring regions dissimilar. We develop a flexible Bayesian approach for learning from spatial data which units are close in an unobserved socio-demographic space and hence which units are similar. As a by-product, the Bayesian approach helps quantify the relative importance of socio-demographic space relative to geographical space. To demonstrate the proposed approach, we present simulations along with an application to county-level data on median household income in the U.S. state of Florida.

stat.ME↗

arXiv2022

Multilevel Network Item Response Modeling for Discovering Differences Between Innovation and Regular School Systems in Korea

The innovation school system in South Korea has been developed in response to the traditional high-pressure school system in South Korea, with a view to cultivating a bottom-up and student-centered educational culture. Despite its ambitious goals, questions have been raised about the success of the innovation school system. Leveraging data from the Gyeonggi Education Panel Study (GEPS) along with advances in the statistical analysis of network data and educational data, we compare the two school systems in more depth. We find that some schools are indeed different from others, and those differences are not detected by conventional multilevel models. Having said that, we do not find much evidence that the innovation school system differs from the regular school system in terms of self-reported mental well-being, although we do detect differences among some schools that appear to be unrelated to the school system.

stat.AP↗

arXiv2021

A semiparametric Bayesian approach to epidemics, with application to the spread of the coronavirus MERS in South Korea in 2015

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modeling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modeling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research.

stat.ME↗

arXiv2021

Bayesian Model Selection for High-Dimensional Ising Models, With Applications to Educational Data

Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific example is psychometrics, which has adapted high-dimensional Ising models from machine learning, with a view to studying the interactions among binary item responses in educational assessments. To estimate high-dimensional Ising models from educational assessment data, $\ell_1$-penalized nodewise logistic regressions have been used. Theoretical results in high-dimensional statistics show that $\ell_1$-penalized nodewise logistic regressions can recover the true interaction structure with high probability, provided that certain assumptions are satisfied. Those assumptions are hard to verify in practice and may be violated, and quantifying the uncertainty about the estimated interaction structure and parameter estimators is challenging. We propose a Bayesian approach that helps quantify the uncertainty about the interaction structure and parameters without requiring strong assumptions, and can be applied to Ising models with thousands of parameters. We demonstrate the advantages of the proposed Bayesian approach compared with $\ell_1$-penalized nodewise logistic regressions by simulation studies and applications to small and large educational data sets with up to 2,485 parameters. Among other things, the simulation studies suggest that the Bayesian approach is more robust against model misspecification due to omitted covariates than $\ell_1$-penalized nodewise logistic regressions.

stat.CO↗

arXiv2020

Mapping unobserved item-respondent interactions: A latent space item response model with interaction map

Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent's and the item's position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results.

stat.ME↗

arXiv2020

Large-scale estimation of random graph models with local dependence

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open problem is how to estimate such models from large networks. A novel approach to large-scale estimation is proposed, taking advantage of the local structure of such models for the purpose of local computing. The main idea is that random graphs with local dependence can be decomposed into subgraphs, which enables parallel computing on subgraphs and suggests a two-step estimation approach. The first step estimates the local structure underlying random graphs. The second step estimates parameters given the estimated local structure of random graphs. Both steps can be implemented in parallel, which enables large-scale estimation. The advantages of the two-step estimation approach are demonstrated by simulation studies with up to 10,000 nodes and an application to a large Amazon product recommendation network with more than 10,000 products.

stat.CO↗

arXiv2019

Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios

Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special cases of ERGMs are generalized linear models (GLMs), Bernoulli random graphs, $β$-models, $p_1$-models, and models related to Markov random fields in spatial statistics and other areas of statistics. While widely used in practice, questions have been raised about the theoretical properties of ERGMs. These include concerns that some ERGMs are near-degenerate and that many ERGMs are non-projective. To address them, careful attention must be paid to model specifications and their underlying assumptions, and in which inferential settings models are employed. As we discuss, near-degeneracy can affect simplistic ERGMs lacking structure, but well-posed ERGMs with additional structure can be well-behaved. Likewise, lack of projectivity can affect non-likelihood-based inference, but likelihood-based inference does not require projectivity. Here, we review well-posed ERGMs along with likelihood-based inference. We first clarify the core statistical notions of "sample" and "population" in the ERGM framework, and separate the process that generates the population graph from the observation process. We then review likelihood-based inference in finite-, super-, and infinite-population scenarios. We conclude with consistency results, and an application to human brain networks

stat.ME↗

arXiv2019

Consistent structure estimation of exponential-family random graph models with block structure

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs with additional structure in the form of block structure. We have shown elsewhere that when the block structure is known, it facilitates consistency results for $M$-estimators of canonical and curved exponential-family random graph models with complex dependence, such as transitivity. In practice, the block structure is known in some applications (e.g., multilevel networks), but is unknown in others. When the block structure is unknown, the first and foremost question is whether it can be recovered with high probability based on a single observation of a random graph with complex dependence. The main consistency results of the paper show that it is possible to do so under weak dependence and smoothness conditions. These results confirm that exponential-family random graph models with block structure constitute a promising direction of statistical network analysis.

math.ST↗

arXiv2018

Concentration and consistency results for canonical and curved exponential-family models of random graphs

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and $M$-estimators of a wide range of canonical and curved exponential-family models of random graphs with local dependence. All results are non-asymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.

math.ST↗