arXiv subjects

Cornelius Fritz

Publications and source records attributed to Cornelius Fritz.

At least 19 recordsLinked to original sources

arXiv2026

A Counting Process View of Relational Event Models: Practical Asymptotics

Relational Event Models (REMs) provide a rigorous framework for analyzing dyadic interactions observed in continuous time, capturing history-dependent dynamics such as triadic closure and reciprocity. Framing REMs through the lens of counting processes embeds the model in a rich theoretical foundation, facilitating its mathematical analysis. While Maximum Likelihood Estimation (MLE) is standard practice for estimating these models, the underlying statistical guarantees rely on specific asymptotic regimes, namely, whether the network size (n), the observational period (T), or both approach infinity. We review the theoretical foundations of such counting-process-based models, formalizing the core assumptions required to achieve asymptotic normality across these different limits. With a specific focus on Cox-type multiplicative models, we detail the circumstances under which these assumptions hold. Supported by simulation studies, we illustrate how structural modeling choices, including temporal windowing and logarithmic transformations, affect empirical coverage and estimator convergence. We thereby derive several guiding principles for specifying such models in realistic contexts, bridging theory and practice.

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↗

arXiv2025

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

Scalable Signed Exponential Random Graph Models under Local Dependence

Traditional network analysis focuses on binary edges, while real-world relationships are more nuanced, encompassing cooperation, neutrality, and conflict. The rise of negative edges in social media discussions spurred interest in analyzing signed interactions, especially in polarized debates. However, the vast data generated by digital networks presents challenges for traditional methods like Stochastic Block Models (SBM) and Exponential Family Random Graph Models (ERGM), particularly due to the homogeneity assumption and global dependence, which become increasingly unrealistic as network size grows. To address this, we propose a novel method that combines the strengths of SBM and ERGM while mitigating their weaknesses by incorporating local dependence based on nonoverlapping blocks. Our approach involves a two-step process: First, decomposing the network into sub-networks using SBM approximation, and, second, estimating parameters using ERGM methods. We validate our method on large synthetic networks and apply it to a signed Wikipedia network of thousands of editors. Through the use of local dependence, we find patterns consistent with structural balance theory.

cs.SI↗

arXiv2025

Guardians of the Regime: Secret Police Formation in Autocracies

Autocrats use secret police to stay in power, as these organizations deter and suppress opposition to their rule. Existing research shows that secret police succeed at this but, surprisingly, also that they are not as ubiquitous in autocracies as one may assume, existing in fewer than half of autocratic country-years. We thus explore under which conditions secret police emerge in dictatorships. For this purpose, we develop a theoretical framework for potential predictors and apply statistical variable selection techniques to identify which of several candidate variables extracted from the literature on state security forces and authoritarian survival hold explanatory power. Our results highlight that secret police are more likely to emerge when rulers face structural, regime-external threats, such as organised anti-system mobilisation and international rivals, or witness successful regime-internal contestation abroad that hints at similar threats at home. But additionally, we find that rulers must have sufficient material resources and personalised power to establish secret police. This research contributes to our understanding of autocrats' institutional choices and authoritarian politics.

cs.CR↗

arXiv2025

Socio-cognitive Networks between Researchers: Investigating Scientific Dualities with the Group-Oriented Relational Hyperevent Model

Understanding why researchers cite certain works remains a key question in the study of scientific networks. Prior research has identified factors such as relevance, group cohesion, and source crediting. However, the interplay between cognitive and social dimensions in citation behavior - often conceptualized as a socio-cognitive network - is frequently overlooked, particularly regarding the intermediary steps that lead to a citation. Since a citation first requires a work to be published by a set of authors, we examine how the structure of coauthorship networks influences citation patterns. To investigate this relationship, we analyze the citation and collaboration behavior of Chilean astronomers from 2013 to 2015 using the Group-Oriented Relational Hyperevent Model, which allows us to study coauthorship and citation networks in a joint framework. Our findings suggest that when selecting which works to cite, authors favor recent research and maintain cognitive continuity across cited works. At the same time, we observe that coherent groups - closely connected coauthors - tend to be co-cited more frequently in subsequent publications, reinforcing the interdependence of collaboration and citation networks.

cs.SI↗

arXiv2025

Scalable Durational Event Models: Application to Physical and Digital Interactions

Durable interactions are increasingly observed in social network analysis with precise timestamps. Phone and video calls, for instance, are events to which a specific duration can be assigned. We term data encoding interactions with start and end times ``durational event data''. Recent advances in data collection have enabled the observation of such data over extended periods and across large populations of actors. Methodologically, we propose the Durational Event Model, an extension of Relational Event Models that decouples the modeling of event incidence from event duration. Computationally, we derive a fast, memory-efficient, and exact block-coordinate ascent algorithm to facilitate large-scale inference. Theoretical complexity analysis and numerical simulations demonstrate the computational superiority of this approach over state-of-the-art methods. We apply the model implemented in the R package redeem to physical and digital interactions among college students in Copenhagen. Our empirical findings reveal that past interactions drive physical interactions, whereas digital interactions are influenced predominantly by friendship ties and prior dyadic contact.

stat.ME↗

arXiv2024

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↗

arXiv2024

How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regression

Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

cs.LG↗

arXiv2024

The 2023/24 VIEWS Prediction Challenge: Predicting the Number of Fatalities in Armed Conflict, with Uncertainty

This draft article outlines a prediction challenge where the target is to forecast the number of fatalities in armed conflicts, in the form of the UCDP `best' estimates, aggregated to the VIEWS units of analysis. It presents the format of the contributions, the evaluation metric, and the procedures, and a brief summary of the contributions. The article serves a function analogous to a pre-analysis plan: a statement of the forecasting models made publicly available before the true future prediction window commences. More information on the challenge, and all data referred to in this document, can be found at https://viewsforecasting.org/research/prediction-challenge-2023.

stat.AP↗

arXiv2024

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↗

arXiv2023

Dependence matters: Statistical models to identify the drivers of tie formation in economic networks

Networks are ubiquitous in economic research on organizations, trade, and many other areas. However, while economic theory extensively considers networks, no general framework for their empirical modeling has yet emerged. We thus introduce two different statistical models for this purpose -- the Exponential Random Graph Model (ERGM) and the Additive and Multiplicative Effects network model (AME). Both model classes can account for network interdependencies between observations, but differ in how they do so. The ERGM allows one to explicitly specify and test the influence of particular network structures, making it a natural choice if one is substantively interested in estimating endogenous network effects. In contrast, AME captures these effects by introducing actor-specific latent variables affecting their propensity to form ties. This makes the latter a good choice if the researcher is interested in capturing the effect of exogenous covariates on tie formation without having a specific theory on the endogenous dependence structures at play. After introducing the two model classes, we showcase them through real-world applications to networks stemming from international arms trade and foreign exchange activity. We further provide full replication materials to facilitate the adoption of these methods in empirical economic research.

stat.ME↗

arXiv2022

All that Glitters is not Gold: Relational Events Models with Spurious Events

As relational event models are an increasingly popular model for studying relational structures, the reliability of large-scale event data collection becomes more and more important. Automated or human-coded events often suffer from non-negligible false-discovery rates in event identification. And most sensor data is primarily based on actors' spatial proximity for predefined time windows; hence, the observed events could relate either to a social relationship or random co-location. Both examples imply spurious events that may bias estimates and inference. We propose the Relational Event Model for Spurious Events (REMSE), an extension to existing approaches for interaction data. The model provides a flexible solution for modeling data while controlling for spurious events. Estimation of our model is carried out in an empirical Bayesian approach via data augmentation. Based on a simulation study, we investigate the properties of the estimation procedure. To demonstrate its usefulness in two distinct applications, we employ this model to combat events from the Syrian civil war and student co-location data. Results from the simulation and the applications identify the REMSE as a suitable approach to modeling relational event data in the presence of spurious events.

stat.ME↗

arXiv2022

Exponential Random Graph Models for Dynamic Signed Networks: An Application to International Relations

Substantive research in the Social Sciences regularly investigates signed networks, where edges between actors are either positive or negative. For instance, schoolchildren can be friends or rivals, just as countries can cooperate or fight each other. This research often builds on structural balance theory, one of the earliest and most prominent network theories, making signed networks one of the most frequently studied matters in social network analysis. While the theorization and description of signed networks have thus made significant progress, the inferential study of tie formation within them remains limited in the absence of appropriate statistical models. In this paper we fill this gap by proposing the Signed Exponential Random Graph Model (SERGM), extending the well-known Exponential Random Graph Model (ERGM) to networks where ties are not binary but negative or positive if a tie exists. Since most networks are dynamically evolving systems, we specify the model for both cross-sectional and dynamic networks. Based on structural hypotheses derived from structural balance theory, we formulate interpretable signed network statistics, capturing dynamics such as "the enemy of my enemy is my friend". In our empirical application, we use the SERGM to analyze cooperation and conflict between countries within the international state system.

cs.SI↗

arXiv2022

deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression

In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our implementation encompasses (1) a modular neural network building system based on the deep learning library \pkg{TensorFlow} for the fusion of various statistical and deep learning approaches, (2) an orthogonalization cell to allow for an interpretable combination of different subnetworks, as well as (3) pre-processing steps necessary to set up such models. The software package allows to define models in a user-friendly manner via a formula interface that is inspired by classical statistical model frameworks such as \pkg{mgcv}. The packages' modular design and functionality provides a unique resource for both scalable estimation of complex statistical models and the combination of approaches from deep learning and statistics. This allows for state-of-the-art predictive performance while simultaneously retaining the indispensable interpretability of classical statistical models.

stat.ML↗

arXiv2022

Modelling the large and dynamically growing bipartite network of German patents and inventors

We analyse the bipartite dynamic network of inventors and patents registered within the main area of electrical engineering in Germany to explore the driving forces behind innovation. The data at hand leads to a bipartite network, where an edge between an inventor and a patent is present if the inventor is a co-owner of the respective patent. Since more than a hundred thousand patents were filed by similarly as many inventors during the observational period, this amounts to a massive bipartite network, too large to be analysed as a whole. Therefore, we decompose the bipartite network by utilising an essential characteristic of the network: most inventors tend to stay active only for a relatively short period, while new ones become active at each point in time. Consequently, the adjacency matrix carries several structural zeros. To accommodate for these, we propose a bipartite variant of the Temporal Exponential Random Graph Model (TERGM) in which we let the actor set vary over time, differentiate between inventors that already submitted patents and those that did not, and account for pairwise statistics of inventors. Our results corroborate the hypotheses that inventor characteristics and knowledge flows play a crucial role in the dynamics of invention.

physics.soc-ph↗

arXiv2022

Statistical modelling of COVID-19 data: Putting Generalised Additive Models to work

Over the course of the COVID-19 pandemic, Generalised Additive Models (GAMs) have been successfully employed on numerous occasions to obtain vital data-driven insights. In this paper we further substantiate the success story of GAMs, demonstrating their flexibility by focusing on three relevant pandemic-related issues. First, we examine the interdepency among infections in different age groups, concentrating on school children. In this context, we derive the setting under which parameter estimates are independent of the (unknown) case-detection ratio, which plays an important role in COVID-19 surveillance data. Second, we model the incidence of hospitalisations, for which data is only available with a temporal delay. We illustrate how correcting for this reporting delay through a nowcasting procedure can be naturally incorporated into the GAM framework as an offset term. Third, we propose a multinomial model for the weekly occupancy of intensive care units (ICU), where we distinguish between the number of COVID-19 patients, other patients and vacant beds. With these three examples, we aim to showcase the practical and "off-the-shelf" applicability of GAMs to gain new insights from real-world data.

stat.AP↗

arXiv2021

On the Interplay of Regional Mobility, Social Connectedness, and the Spread of COVID-19 in Germany

Since the primary mode of respiratory virus transmission is person-to-person interaction, we are required to reconsider physical interaction patterns to mitigate the number of people infected with COVID-19. While research has shown that non-pharmaceutical interventions (NPI) had an evident impact on national mobility patterns, we investigate the relative regional mobility behaviour to assess the effect of human movement on the spread of COVID-19. In particular, we explore the impact of human mobility and social connectivity derived from Facebook activities on the weekly rate of new infections in Germany between March 3rd and June 22nd, 2020. Our results confirm that reduced social activity lowers the infection rate, accounting for regional and temporal patterns. The extent of social distancing, quantified by the percentage of people staying put within a federal administrative district, has an overall negative effect on the incidence of infections. Additionally, our results show spatial infection patterns based on geographic as well as social distances.

stat.AP↗