arXiv subjects

Eric Yanchenko

Publications and source records attributed to Eric Yanchenko.

18 recordsLinked to original sources

arXiv2026

Core-periphery identification in massive networks

Modern networks can be huge with millions or even billions of nodes and edges. Thus, algorithms must be capable of scaling to such large networks in order to be practically useful. In this work, we are interested in developing an algorithm to identify core-periphery structure in massive networks. Core-periphery structure is a meso-scale feature where nodes are grouped into a densely connected core or sparsely connected periphery. To identify such structures in large networks, we propose a divide-and-conquer algorithm. The key feature of our algorithm is leveraging the edge list representation of the network, instead of the adjacency matrix, as it tends to be faster and makes a more efficient use of memory. We apply the proposed algorithm to synthetic and real-world data, notably demonstrating its performance on a real-world network with almost 14 million edges without loading the entire network into memory.

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arXiv2026

Universal Inference for model selection on networks

Model selection and hypothesis testing are important tasks on networks. A key challenge lies in the inherent dependence in network data, as well as the fact that typically only a single realization is observed. As a result, many existing methods must be carefully tailored to specific models and only come with asymptotic theoretical guarantees. In this work, however, we propose a general model selection framework using Universal Inference, making our method widely applicable to various testing scenarios. Since Universal Inference requires two sets of data, we employ edge sampling to obtain proper networks with tractable dependence. We prove that the proposed statistic is an e-value, thus controlling the type I error rate in finite samples under nearly any hypothesis test. To our knowledge, this is the first Universal Inference-type statistic constructed from dependent splits of data as well as the first finite-sample testing guarantee for hypothesis testing on networks. We also prove that the logarithm of the test statistic diverges to positive infinity under various alternative models. On simulated and real-world networks, the proposed method performs well on tasks such as choosing the random graph model and the number of communities.

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arXiv2025

Statistical inference for core-periphery structures

Core-periphery (CP) structure is an important meso-scale network property where nodes group into a small, densely interconnected {core} and a sparse {periphery} whose members primarily connect to the core rather than to each other. While this structure has been observed in numerous real-world networks, there has been minimal statistical formalization of it. In this work, we develop a statistical framework for CP structures by introducing a model-agnostic and generalizable population parameter which quantifies the strength of a CP structure at the level of the data-generating mechanism. We study this parameter under four canonical random graph models and establish theoretical guarantees for label recovery, including exact label recovery. Next, we construct intersection tests for validating the presence and strength of a CP structure under multiple null models, and prove theoretical guarantees for type I error and power. These tests provide a formal distinction between exogenous (or induced) and endogenous (or intrinsic) CP structure in heterogeneous networks, enabling a level of structural resolution that goes beyond merely detecting the presence of CP structure. The proposed methods show excellent performance on synthetic data, and our applications demonstrate that statistically significant CP structure is somewhat rare in real-world networks.

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arXiv2025

Hypothesis testing for community structure in temporal networks using e-values

Community structure in networks naturally arises in various applications. But while the topic has received significant attention for static networks, the literature on community structure in temporally evolving networks is more scarce. In particular, there are currently no statistical methods available to test for the presence of community structure in a sequence of networks evolving over time. In this work, we propose a simple yet powerful test using e-values, an alternative to p-values that is more flexible in certain ways. Specifically, an e-value framework retains valid testing properties even after combining dependent information, a relevant feature in the context of testing temporal networks. We apply the proposed test to synthetic and real-world networks, demonstrating various features inherited from the e-value formulation and exposing some of the inherent difficulties of testing on temporal networks.

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arXiv2025

A label-switching algorithm for fast core-periphery identification

Core-periphery (CP) structure is frequently observed in networks where the nodes form two distinct groups: a small, densely interconnected core and a sparse periphery. Borgatti and Everett (2000) proposed one of the most popular methods to identify and quantify CP structure by comparing the observed network with an ``ideal'' CP structure. While this metric has been widely used, an improved algorithm is still needed. In this work, we detail a greedy, label-switching algorithm to identify CP structure that is both fast and accurate. By leveraging a mathematical reformulation of the CP metric, our proposed heuristic offers an order-of-magnitude improvement on the number of operations compared to a naive implementation. We prove that the algorithm monotonically ascends to a local maximum while consistently yielding solutions within 90% of the global optimum on small toy networks. On synthetic networks, our algorithm exhibits superior classification accuracies and run-times compared to a popular competing method, and on one-real world network, it is 340 times faster.

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arXiv2025

Pseudo-R2D2 prior for high-dimensional ordinal regression

Ordinal regression with a high-dimensional covariate space has many important application areas including gene expression studies. The lack of an intrinsic numeric value associated with ordinal responses, however, makes methods based on continuous data, like linear regression, inappropriate. In this work, we extend the R2D2 prior framework to the high-dimensional ordinal setting. Since the $R^2$ definition used in the R2D2 prior relies on means and variances, it cannot be used for ordinal regression as these two quantities are not suitable for such data. Instead, by simulating data and using McFadden's coefficient-of-determination ($R^2_M$), we show that a generalized inverse Gaussian prior distribution on the global variance parameter approximately induces a beta prior distribution on $R^2_M$. The proposed prior can be implemented in $\texttt{Stan}$ and an $\texttt{R}$ package is also developed. Our method demonstrates excellent inference properties on simulated data, as well as yielding accurate predictions when applied to a liver tissue gene expression dataset.

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arXiv2024

The Group R2D2 Shrinkage Prior for Sparse Linear Models with Grouped Covariates

Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping structure. This paper proposes a novel extension of the $R^2$-induced Dirichlet Decomposition (R2D2) prior to accommodate grouped variable selection in linear regression models. The proposed method, called the Group R2D2 prior, employs a Dirichlet prior distribution on the coefficient of determination for each group, allowing for a flexible and adaptive shrinkage that operates at both group and individual variable levels. This approach improves the original R2D2 prior to handle grouped predictors, providing a balance between within-group dependence and group-level sparsity. We present several theoretical properties of this proposed prior distribution while also developing a Markov Chain Monte Carlo algorithm. Through simulation studies and real-data analysis, we demonstrate that our method outperforms traditional shrinkage priors in terms of both estimation accuracy, inference and prediction.

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arXiv2024

Mediation analysis of community context effects on heart failure using the survival R2D2 prior

Congestive heart failure (CHF) is a leading cause of morbidity, mortality and healthcare costs, impacting $>$23 million individuals worldwide. Large electronic health records data provide an opportunity to improve clinical management of diseases, but statistical inference on large amounts of relevant personal data is still challenging. Thus, accurately identifying influential risk factors is pivotal to reducing information dimensionality. Bayesian variable selection in survival regression is a common approach towards solving this problem. Here, we propose placing a beta prior directly on the model coefficient of determination (Bayesian $R^2$), which induces a prior on the global variance of the predictors and provides shrinkage. Through reparameterization using an auxiliary variable, we are able to update a majority of the parameters with Gibbs sampling, simplifying computation and quickening convergence. Performance gains over competing variable selection methods are showcased through an extensive simulation study. Finally, the method is applied in a mediation analysis to identify community context attributes impacting time to first congestive heart failure diagnosis of patients enrolled in University of North Carolina Cardiovascular Device Surveillance Registry. The model has high predictive performance and we find that factors associated with higher socioeconomic inequality increase risk of heart failure.

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arXiv2024

Oral exams in introductory statistics class with non-native English speakers

Oral exams are a powerful tool to assess student's learning. This is particularly important in introductory statistics classes where students struggle to grasp various topics like the interpretation of probability, $p$-values and more. The challenge of acquiring conceptual understanding is only heightened when students are learning in a second language. In this paper, I share my experience administering oral exams to an introductory statistics class of non-native English speakers at a Japanese university. I explain the context of the university and course, before detailing the exam. Of particular interest is the relationship between exam performance and English proficiency. The results showed little relationship between the two, meaning the exam seemed to truly test student's statistical knowledge rather than their English ability. I close with encouragements and recommendations for practitioners hoping to implement similar oral exams, focusing on the unique difficulties faced by students not learning in their mother tongue.

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arXiv2024

Graph sub-sampling for divide-and-conquer algorithms in large networks

As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks has become a popular approach. Due to a network's inherent inter-connectedness, however, sub-sampling is not a trivial task. While this problem has gained popularity in recent years, it has not received sufficient attention from the statistics community. In this work, we provide a thorough comparison of seven graph sub-sampling algorithms by applying them to divide-and-conquer algorithms for community structure and core-periphery (CP) structure. After discussing the various algorithms and sub-sampling routines, we derive theoretical results for the mis-classification rate of the divide-and-conquer algorithm for CP structure under various sub-sampling schemes. We then perform extensive experiments on both simulated and real-world data to compare the various methods. For the community detection task, we found that sampling nodes uniformly at random yields the best performance, but that sometimes the base algorithm applied to the entire network yields better results both in terms of identification and computational time. For CP structure on the other hand, there was no single winner, but algorithms which sampled core nodes at a higher rate consistently outperformed other sampling routines, e.g., random edge sampling and random walk sampling. Unlike community detection, the CP divide-and-conquer algorithm tends to yield better identification results while also being faster than the base algorithm. The varying performance of the sampling algorithms on different tasks demonstrates the importance of carefully selecting a sub-sampling routine for the specific application.

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arXiv2023

BOPIM: Bayesian Optimization for influence maximization on temporal networks

The goal of influence maximization (IM) is to select a small set of seed nodes which maximizes the spread of influence on a network. In this work, we propose BOPIM, a Bayesian Optimization (BO) algorithm for IM on temporal networks. The IM task is well-suited for a BO solution due to its expensive and complicated objective function. There are at least two key challenges, however, that must be overcome, primarily due to the inputs coming from a cardinality-constrained, non-Euclidean, combinatorial space. The first is constructing the kernel function for the Gaussian Process regression. We propose two kernels, one based on the Hamming distance between seed sets and the other leveraging the Jaccard coefficient between node's neighbors. The second challenge is the acquisition function. For this, we use the Expected Improvement function, suitably adjusting for noise in the observations, and optimize it using a greedy algorithm to account for the cardinality constraint. In numerical experiments on real-world networks, we prove that BOPIM outperforms competing methods and yields comparable influence spreads to a gold-standard greedy algorithm while being as much as ten times faster. In addition, we find that the Hamming kernel performs favorably compared to the Jaccard kernel in nearly all settings, a somewhat surprising result as the former does not explicitly account for the graph structure. Finally, we demonstrate two ways that the proposed method can quantify uncertainty in optimal seed sets. To our knowledge, this is the first attempt to look at uncertainty in the seed sets for IM.

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arXiv2023

Influence maximization on temporal networks: a review

Influence maximization (IM) is an important topic in network science where a small seed set is chosen to maximize the spread of influence on a network. Recently, this problem has attracted attention on temporal networks where the network structure changes with time. IM on such dynamically varying networks is the topic of this review. We first categorize methods into two main paradigms: single and multiple seeding. In single seeding, nodes activate at the beginning of the diffusion process, and most methods either efficiently estimate the influence spread and select nodes with a greedy algorithm, or use a node-ranking heuristic. Nodes activate at different time points in the multiple seeding problem, via either sequential seeding, maintenance seeding or node probing paradigms. Throughout this review, we give special attention to deploying these algorithms in practice while also discussing existing solutions for real-world applications. We conclude by sharing important future research directions and challenges.

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arXiv2023

Link prediction for ex ante influence maximization on temporal networks

Influence maximization (IM) is the task of finding the most important nodes in order to maximize the spread of influence or information on a network. This task is typically studied on static or temporal networks where the complete topology of the graph is known. In practice, however, the seed nodes must be selected before observing the future evolution of the network. In this work, we consider this realistic ex ante setting where $p$ time steps of the network have been observed before selecting the seed nodes. Then the influence is calculated after the network continues to evolve for a total of $T>p$ time steps. We address this problem by using statistical, non-negative matrix factorization and graph neural networks link prediction algorithms to predict the future evolution of the network and then apply existing influence maximization algorithms on the predicted networks. Additionally, the output of the link prediction methods can be used to construct novel IM algorithms. We apply the proposed methods to eight real-world and synthetic networks to compare their performance using the Susceptible-Infected (SI) diffusion model. We demonstrate that it is possible to construct quality seed sets in the ex ante setting as we achieve influence spread within 87\% of the optimal spread on seven of eight network. In many settings, choosing seed nodes based only historical edges provides results comparable to the results treating the future graph snapshots as known. The proposed heuristics based on the link prediction model are also some of the best-performing methods. These findings indicate that, for these eight networks under the SI model, the latent process which determines the most influential nodes may not have large temporal variation. Thus, knowing the future status of the network is not necessary to obtain good results for ex ante IM.

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arXiv2023

Spatial regression modeling via the R2D2 framework

Spatially dependent data arises in many applications, and Gaussian processes are a popular modelling choice for these scenarios. While Bayesian analyses of these problems have proven to be successful, selecting prior distributions for these complex models remains a difficult task. In this work, we propose a principled approach for setting prior distributions on model variance components by placing a prior distribution on a measure of model fit. In particular, we derive the distribution of the prior coefficient of determination. Placing a beta prior distribution on this measure induces a generalized beta prime prior distribution on the global variance of the linear predictor in the model. This method can also be thought of as shrinking the fit towards the intercept-only (null) model. We derive an efficient Gibbs sampler for the majority of the parameters and use Metropolis-Hasting updates for the others. Finally, the method is applied to a marine protection area data set. We estimate the effect of marine policies on biodiversity and conclude that no-take restrictions lead to a slight increase in biodiversity and that the majority of the variance in the linear predictor comes from the spatial effect.\vspace{12pt}

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arXiv2022

Quantifying the presence/absence of meso-scale structures in networks

Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative communities, disassortative communities and core-periphery. We then leverage these definitions and a Bayesian framework to quantify the presence/absence of each structure in a network. This allows for probabilistic statements about the network structure as well as uncertainty estimates of the group labels and edge probabilities. The method is applied to real-world networks, yielding provocative results about well-known network data sets.

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arXiv2022

Core-periphery structure in networks: a statistical exposition

Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it has not received sufficient attention in the statistics community. In this expository article, our goal is to raise awareness about this topic and encourage statisticians to address the many open inference problems in this area. To this end, we first summarize the current research landscape by reviewing the metrics and models that have been used for quantitative studies on core-periphery structure. Next, we formulate and explore various inferential problems in this context, such as estimation, hypothesis testing, and Bayesian inference, and discuss related computational techniques. We also outline the multidisciplinary scientific impact of core-periphery structure in a number of real-world networks. Throughout the article, we provide our own interpretation of the literature from a statistical perspective, with the goal of prioritizing open problems where contribution from the statistics community will be most effective and important.

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arXiv2021

The R2D2 Prior for Generalized Linear Mixed Models

In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to place a prior on a summary measure of the model instead. In this work, we propose a prior on the model fit, as measured by a Bayesian coefficient of determination ($R^2)$, which then induces a prior on the individual parameters. We achieve this by placing a beta prior on $R^2$ and then deriving the induced prior on the global variance parameter for generalized linear mixed models. We derive closed-form expressions in many scenarios and present several approximation strategies when an analytic form is not possible and/or to allow for easier computation. In these situations, we suggest approximating the prior by using a generalized beta prime distribution and provide a simple default prior construction scheme. This approach is quite flexible and can be easily implemented in standard Bayesian software. Lastly, we demonstrate the performance of the method on simulated and real-world data, where the method particularly shines in high-dimensional settings, as well as modeling random effects.

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arXiv2021

A generalized hypothesis test for community structure in networks

Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibit statistically meaningful community structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world data sets.

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