Stochastic Block Model Research Articles

Communities in C. elegans connectome through the prism of non-backtracking walks

The fundamental relationship between the mesoscopic structure of neuronal circuits and organismic functions they subserve is one of the major challenges in contemporary neuroscience. Formation of structurally connected modules of neurons enacts the conversion from single-cell firing to large-scale behaviour of an organism, highlighting the importance of their accurate profiling in the data. While connectomes are typically characterized by significant sparsity of neuronal connections, recent advances in network theory and machine learning have revealed fundamental limitations of traditionally used community detection approaches in cases where the network is sparse. Here we studied the optimal community structure in the structural connectome of Caenorhabditis elegans, for which we exploited a non-conventional approach that is based on non-backtracking random walks, virtually eliminating the sparsity issue. In full agreement with the previous asymptotic results, we demonstrated that non-backtracking walks resolve the ground truth annotation into clusters on stochastic block models (SBM) with the size and density of the connectome better than the spectral methods related to simple random walks. Based on the cluster detectability threshold, we determined that the optimal number of modules in a recently mapped connectome of C. elegans is 10, which precisely corresponds to the number of isolated eigenvalues in the spectrum of the non-backtracking flow matrix. The discovered communities have a clear interpretation in terms of their functional role, which allows one to discern three structural compartments in the worm: the Worm Brain (WB), the Worm Movement Controller (WMC), and the Worm Information Flow Connector (WIFC). Broadly, our work provides a robust network-based framework to reveal mesoscopic structures in sparse connectomic datasets, paving way to further investigation of connectome mechanisms for different functions.

Untangling pair synergy in the evolution of collaborative scientific impact

Synergy, or team chemistry, is an elusive concept that explains how collaboration is able to yield outcomes beyond expectations. Here, we reveal its presence and underlying mechanisms in pairwise scientific collaboration by reconstructing the publication histories of 560,689 individual scientists and 1,026,196 pairs of scientists. We quantify pair synergy by extracting the non-additive effects of collaboration on scientific impact, which are not confounded by prior collaboration experience or luck. We employ a network inference methodology with the stochastic block model to investigate the mechanism of pair synergy and its connection to individual attributes. The inferred block structure, derived solely from the observed types of synergy, can anticipate an undetermined type of synergy between two scientists who have never collaborated. This suggests that synergy arises from a suitable combination of certain, yet unidentified, individual characteristics. Furthermore, the most relevant to pair synergy is research interest, although its diversity does not lead to complementarity across all disciplines. Our results pave the way for understanding the dynamics of collaborative success in science and unlocking the hidden potential of collaboration by matchmaking between scientists.

Aberrant Functional Connectivity in Core–Periphery Structure Based on WSBM in ADHD

Objective: Brain network studies have revealed that the community structure of ADHD is altered. However, these studies have only focused on modular community structure, ignoring the core–periphery community structure. Method: This paper employed the weighted stochastic block model to divide the functional connectivity (FC) into 10 communities. And we adopted core score to define the core–periphery structure of FC. Finally, connectivity strength (CS) and disruption index (DI) were used to evaluate the changes of core–periphery structure in ADHD. Results: The core community of visual network showed reduced CS and a positive value of DI, while the CS of periphery community was enhanced. In addition, the interaction between core communities (involving the sensorimotor and visual network) and periphery community of attention network showed increased CS and a negative valve of DI. Conclusion: Anomalies in core–periphery community structure provide a new perspective for understanding the community structure of ADHD.

Two-sample test of stochastic block models

In this paper, we consider the problem of two-sample test of large networks with community structures. A test statistic is proposed based on the maximum entry of the difference between the two adjacency matrices. Asymptotic null distribution is derived, and the asymptotic power guarantee against the alternative hypothesis is provided. The simulations and real data examples show that the proposed test statistic performs well.

FMC2 model based perception grading for dark insurgent network analysis.

The burgeoning role of social network analysis (SNA) in various fields raises complex challenges, particularly in the analysis of dark and dim networks involved in illicit activities. Existing models like the stochastic block model (SBM), exponential graph model (EGM), and latent space model (LSM) are limited in scope, often only suitable for one-mode networks. This article introduces a novel fuzzy multiple criteria multiple constraint model (FMC2) tailored for community detection in two-mode networks, which are particularly common in dark networks. The proposed method quantitatively determines the relationships between nodes based on a probabilistic measure and uses distance metrics to identify communities within the network. Moreover, the model establishes fuzzy boundaries to differentiate between the most and least influential nodes. We validate the efficacy of FMC2 using the Noordin Terrorist dataset and conduct extensive simulations to evaluate performance metrics. The results demonstrate that FMC2 not only effectively identifies communities but also ranks influential nodes within them, contributing to a nuanced understanding of complex networks. The method promises broad applicability and adaptability, particularly in intelligence and security domains where identifying influential actors within covert networks is critical.

Bayesian Learning of Graph Substructures

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing interest in inferring more complex structures, such as communities, for multiple reasons, including more effective information retrieval and better interpretability. Stochastic blockmodels offer a powerful tool to detect such structure in a network. We thus propose to exploit advances in random graph theory and embed them within the graphical models framework. A consequence of this approach is the propagation of the uncertainty in graph estimation to large-scale structure learning. We consider Bayesian nonparametric stochastic blockmodels as priors on the graph. We extend such models to consider clique-based blocks and to multiple graph settings introducing a novel prior process based on a Dependent Dirichlet process. Moreover, we devise a tailored computation strategy of Bayes factors for block structure based on the Savage-Dickey ratio to test for presence of larger structure in a graph. We demonstrate our approach in simulations as well as on real data applications in finance and transcriptomics.

The Spread of Beliefs in Partially Modularized Communities

Many life-influencing social networks are characterized by considerable informational isolation. People within a community are far more likely to share beliefs than people who are part of different communities. The spread of useful information across communities is impeded by echo chambers (far greater connectivity within than between communities) and filter bubbles (more influence of beliefs by connected neighbors within than between communities). We apply the tools of network analysis to organize our understanding of the spread of beliefs across modularized communities and to predict the effect of individual and group parameters on the dynamics and distribution of beliefs. In our Spread of Beliefs in Modularized Communities (SBMC) framework, a stochastic block model generates social networks with variable degrees of modularity, beliefs have different observable utilities, individuals change their beliefs on the basis of summed or average evidence (or intermediate decision rules), and parameterized stochasticity introduces randomness into decisions. SBMC simulations show surprising patterns; for example, increasing out-group connectivity does not always improve group performance, adding randomness to decisions can promote performance, and decision rules that sum rather than average evidence can improve group performance, as measured by the average utility of beliefs that the agents adopt. Overall, the results suggest that intermediate degrees of belief exploration are beneficial for the spread of useful beliefs in a community, and so parameters that pull in opposite directions on an explore–exploit continuum are usefully paired.

Generative models for two-ground-truth partitions in networks.

A myriad of approaches have been proposed to characterize the mesoscale structure of networks most often as a partition based on patterns variously called communities, blocks, or clusters. Clearly, distinct methods designed to detect different types of patterns may provide a variety of answers' to the networks mesoscale structure. Yet even multiple runs of a given method can sometimes yield diverse and conflicting results, producing entire landscapes of partitions which potentially include multiple (locally optimal) mesoscale explanations of the network. Such ambiguity motivates a closer look at the ability of these methods to find multiple qualitatively different "ground truth" partitions in a network. Here we propose the stochastic cross-block model (SCBM), a generative model which allows for two distinct partitions to be built into the mesoscale structure of a single benchmark network. We demonstrate a use case of the benchmark model by appraising the power of stochastic block models (SBMs) to detect implicitly planted coexisting bicommunity and core-periphery structures of different strengths. Given our model design and experimental setup, we find that the ability to detect the two partitions individually varies by SBM variant and that coexistence of both partitions is recovered only in a very limited number of cases. Our findings suggest that in most instances only one-in some way dominating-structure can be detected, even in the presence of other partitions. They underline the need for considering entire landscapes of partitions when different competing explanations exist and motivate future research to advance partition coexistence detection methods. Our model also contributes to the field of benchmark networks more generally by enabling further exploration of the ability of new and existing methods to detect ambiguity in the mesoscale structure of networks.

Modelling animal network data in R using STRAND.

There have been recent calls for wider application of generative modelling approaches in applied social network analysis. At present, however, it remains difficult for typical end users-for example, field researchers-to implement generative network models, as there is a dearth of openly available software packages that make application of such models as simple as other, permutation-based approaches. Here, we outline the STRAND R package, which provides a suite of generative models for Bayesian analysis of animal social network data that can be implemented using simple, base R syntax. To facilitate ease of use, we provide a tutorial demonstrating how STRAND can be used to model proportion, count or binary network data using stochastic block models, social relation models or a combination of the two modelling frameworks. STRAND facilitates the application of generative network models to a broad range of data found in the animal social networks literature.

HB-DSBM: Modeling the Dynamic Complex Networks From Community Level to Node Level.

A variety of methods have been proposed for modeling and mining dynamic complex networks, in which the topological structure varies with time. As the most popular and successful network model, the stochastic block model (SBM) has been extended and applied to community detection, link prediction, anomaly detection, and evolution analysis of dynamic networks. However, all current models based on the SBM for modeling dynamic networks are designed at the community level, assuming that nodes in each community have the same dynamic behavior, which usually results in poor performance on temporal community detection and loses the modeling of node abnormal behavior. To solve the above-mentioned problem, this article proposes a hierarchical Bayesian dynamic SBM (HB-DSBM) for modeling the node-level and community-level dynamic behavior in a dynamic network synchronously. Based on the SBM, we introduce a hierarchical Dirichlet generative mechanism to associate the global community evolution with the microscopic transition behavior of nodes near-perfectly and generate the observed links across the dynamic networks. Meanwhile, an effective variational inference algorithm is developed and we can easy to infer the communities and dynamic behaviors of the nodes. Furthermore, with the two-level evolution behaviors, it can identify nodes or communities with abnormal behavior. Experiments on simulated and real-world networks demonstrate that HB-DSBM has achieved state-of-the-art performance on community detection and evolution. In addition, abnormal evolutionary behavior and events on dynamic networks can be effectively identified by our model.

Characterizing phonemic fluency by transfer learning with deep language models.

Though phonemic fluency tasks are traditionally indexed by the number of correct responses, the underlying disorder may shape the specific choice of words-both correct and erroneous. We report the first comprehensive qualitative analysis of incorrect and correct words generated on the phonemic ('S') fluency test, in a large sample of patients (n = 239) with focal, unilateral frontal or posterior lesions and healthy controls (n = 136). We conducted detailed qualitative analyses of the single words generated in the phonemic fluency task using categorical descriptions for different types of errors, low-frequency words and clustering/switching. We further analysed patients' and healthy controls' entire sequences of words by employing stochastic block modelling of Generative Pretrained Transformer 3-based deep language representations. We conducted predictive modelling to investigate whether deep language representations of word sequences improved the accuracy of detecting the presence of frontal lesions using the phonemic fluency test. Our qualitative analyses of the single words generated revealed several novel findings. For the different types of errors analysed, we found a non-lateralized frontal effect for profanities, left frontal effects for proper nouns and permutations and a left posterior effect for perseverations. For correct words, we found a left frontal effect for low-frequency words. Our novel large language model-based approach found five distinct communities whose varied word selection patterns reflected characteristic demographic and clinical features. Predictive modelling showed that a model based on Generative Pretrained Transformer 3-derived word sequence representations predicted the presence of frontal lesions with greater fidelity than models of native features. Our study reveals a characteristic pattern of phonemic fluency responses produced by patients with frontal lesions. These findings demonstrate the significant inferential and diagnostic value of characterizing qualitative features of phonemic fluency performance with large language models and stochastic block modelling.

Monitoring networks with overlapping communities based on latent mixed-membership stochastic block model

Monitoring networks with overlapping communities based on latent mixed-membership stochastic block model

On the efficacy of higher-order spectral clustering under weighted stochastic block models

Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. Several works have studied the community detection problem–a fundamental problem in network analysis at the level of motifs. In particular, the higher-order spectral clustering has been developed, where the notion of motif adjacency matrix is introduced as the algorithm's input. However, how the higher-order spectral clustering works and when it performs better than its edge-based counterpart remain largely unknown. To elucidate these problems, the higher-order spectral clustering is investigated from a statistical perspective. The clustering performance of the higher-order spectral clustering is theoretically studied under a weighted stochastic block model, and the resulting bounds are compared with the corresponding results of the edge-based spectral clustering. The upper bounds and simulations show that when the network is dense and the edge weights have a weak signal, higher-order spectral clustering can lead to a performance gain in clustering. Real data experiments also corroborate the merits of higher-order spectral clustering.

Combinatorial-Probabilistic Trade-Off: P-Values of Community Property Test in the Stochastic Block Models

In this paper, we propose an inferential framework testing the general community combinatorial properties of the stochastic block model. Instead of estimating the community assignments, we aim to test the hypothesis on whether a certain community property is satisfied and provide p-values to assess the statistical uncertainty. For instance, we propose to test whether a given set of nodes belong to the same community or whether different network communities have the same size. We present a general inferential framework that can be applied to all symmetric community properties. To ease the challenges caused by the combinatorial nature of community properties, we develop a novel shadowing bootstrap testing method. By utilizing the symmetry, our method can find a shadowing representative of the true assignment and the number of assignments to be tested in the alternative can be largely reduced. In theory, we introduce a combinatorial distance between two community classes and show a combinatorial-probabilistic trade-off phenomenon in the community property test. Our test is honest as long as the product of the combinatorial distance between two community classes and the probabilistic distance between two assignment probabilities is sufficiently large. On the other hand, we show that such a trade-off also exists in the information-theoretic lower bound of the community property test. We also implement numerical experiments on both the synthetic data and the Protein-Protein Interaction networks to show the validity of our method.

Large population limits of Markov processes on random networks

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each discrete state in the system, or in certain subsystems, and general conditions for the convergence of the collective variable dynamics to a mean-field ordinary differential equation are proved. We discuss the convergence to this mean-field limit for a continuous-time noisy version of the so-called “voter model” on Erdős–Rényi random graphs, on the stochastic block model, and on random regular graphs. Moreover, a heterogeneous population of agents is studied.

BRAIN TUMOUR GENETIC NETWORK SIGNATURES SUPERIORLY FORECAST SURVIVAL

Abstract AIMS Gliomas typically exhibit a spectrum of genetic mutations, reflecting multiple, potentially complex interactions across distinct molecular pathways. Predicting disease evolution and prescribing individually optimal treatment plausibly requires statistical models complex enough to capture the intricate genetic structure underpinning oncogenesis. METHOD Here we formalize this task as the discovery of distinct patterns of connectivity within network representations of the interactions between genetic loci. Evaluating multi-institutional clinical, genetic, and outcome data from 4023 consecutive patients over a 14-year period, we employ Bayesian stochastic block modelling to reveal a hierarchical network structure of tumour genetic interactions spanning glioblastoma, oligodendroglioma, and astrocytoma. RESULTS We show that this structure not only identifies diagnosis but predicts patient survival with greater fidelity than the latest WHO tumour classification or linear models of genetic features. For example, a diagnosis of IDH- wildtype glioblastoma yielded median survivals varying from 289 days in patients with the signature of marked EGFR amplification, MGMT methylation, and histone mutations, to 425 days in those with the signature of TERT mutations, histone, and EGFR wild-types, and variable MGMT methylation. CONCLUSIONS Our findings illuminate the complex dependence between features across the genetic landscape of brain tumours and show network analysis reveals distinct signatures of survival with better prognostic fidelity than current gold standard diagnostic categories, paving the way for personalised prognostication.

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.

Forcing generalised quasirandom graphs efficiently

AbstractWe study generalised quasirandom graphs whose vertex set consists of$q$parts (of not necessarily the same sizes) with edges within each part and between each pair of parts distributed quasirandomly; such graphs correspond to the stochastic block model studied in statistics and network science. Lovász and Sós showed that the structure of such graphs is forced by homomorphism densities of graphs with at most$(10q)^q+q$vertices; subsequently, Lovász refined the argument to show that graphs with$4(2q+3)^8$vertices suffice. Our results imply that the structure of generalised quasirandom graphs with$q\ge 2$parts is forced by homomorphism densities of graphs with at most$4q^2-q$vertices, and, if vertices in distinct parts have distinct degrees, then$2q+1$vertices suffice. The latter improves the bound of$8q-4$due to Spencer.

Brain tumour genetic network signatures of survival.

Tumour heterogeneity is increasingly recognized as a major obstacle to therapeutic success across neuro-oncology. Gliomas are characterized by distinct combinations of genetic and epigenetic alterations, resulting in complex interactions across multiple molecular pathways. Predicting disease evolution and prescribing individually optimal treatment requires statistical models complex enough to capture the intricate (epi)genetic structure underpinning oncogenesis. Here, we formalize this task as the inference of distinct patterns of connectivity within hierarchical latent representations of genetic networks. Evaluating multi-institutional clinical, genetic and outcome data from 4023 glioma patients over 14 years, across 12 countries, we employ Bayesian generative stochastic block modelling to reveal a hierarchical network structure of tumour genetics spanning molecularly confirmed glioblastoma, IDH-wildtype; oligodendroglioma, IDH-mutant and 1p/19q codeleted; and astrocytoma, IDH-mutant. Our findings illuminate the complex dependence between features across the genetic landscape of brain tumours and show that generative network models reveal distinct signatures of survival with better prognostic fidelity than current gold standard diagnostic categories.

Statistical clustering of documents via stochastic blockmodels

ABSTRACT As the online market grows rapidly, people are relying more on product review when they purchase the product. Hence, many companies and researchers are interested in analyzing product review which essentially a text data. In the current literature, it is common to use only text analysis tools to analyze text dataset. But in our work, we propose a method that utilizes both text analysis method such as topic modeling and statistical network model to build network among individuals and find interesting communities. We introduce a promising framework that incorporates topic modeling technique to define the edges among the individuals and form a network and uses stochastic blockmodels (SBM) to find the communities. The power of our proposed method is demonstrated in real-world application to Amazon product review dataset.