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AbstractIn recent years, large networks are routinely used to represent data from many scientific fields. Statistical analysis of these networks, such as estimation and hypothesis testing, has received considerable attention. However, most of the methods proposed in the literature are computationally expensive for large networks. In this paper, we propose a subsampling-based method to reduce the computational cost of estimation and two-sample hypothesis testing. The idea is to divide the network into smaller subgraphs with an overlap region, then draw inference based on each subgraph, and finally combine the results together. We first develop the subsampling method for random dot product graph models, and establish theoretical consistency of the proposed method. Then we extend the subsampling method to a more general setup and establish similar theoretical properties. We demonstrate the performance of our methods through simulation experiments and real data analysis. Supplemental materials for the article are available online. The code is available in the following GitHub repository: https://github.com/kchak19/SubsampleTestingNetwork. [ABSTRACT FROM AUTHOR]

This article considers the change detection problem for one-dimensional observation sequences and dynamic network observation sequences. Since for network data, especially for large-scale network data, it is unrealistic to obtain the underlying distribution or underlying probabilistic structure. In this view, we consider a weighted sum approach with constraint for change detection. The purpose of the constraint is to highlight the changes, thus the method proposed has better performance for small shift. Meanwhile, different metrics for network data are suitable for different types of changes, the detection ability of L1-norm is better for dense change, and the detection ability of max-norm is better for sparse change. A parallel multi-chart is proposed as a guidance for improving the performance of change detection for different types of changes. Furthermore, the theoretical results are illustrated numerically on one-dimensional observation sequences and dynamic network observation sequences. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach that combines dynamic linear models applied to graph data and variable selection through spike-and-slab priors. The new class of models, called Dynamic Graphical Variable Selection, is used to infer effective connectivity in certain brain regions allowing both connectivity weights and graphical structure to vary over time. One advantage of our method is that as the graphical structure is estimated inferentially, the computational cost is reduced. That way our methodology can accommodate high-dimensional data, such as large networks observed through long periods of time. We illustrate our methodology via numerical experiments with simulated and synthetic data, and then applied to fNIRS real data. The obtained results showed that the static version of our model is competitive against previous methodologies and demands a lower computational cost. Our model is more flexible than the previous methodologies by allowing the graphical structure to vary over time. [ABSTRACT FROM AUTHOR]

There has been an increasing interest in fraud detection methods, driven by new regulations and by the financial losses linked to fraud. One of the state-of-the-art methods to fight fraud is network analytics. Network analytics leverages the interactions between different entities to detect complex patterns that are indicative of fraud. However, network analytics has only recently been applied to fraud detection in the actuarial literature. Although it shows much potential, many network methods are not yet applied. This paper extends the literature in two main ways. First, we review and apply multiple methods in the context of insurance fraud and assess their predictive power against each other. Second, we analyse the added value of network features over intrinsic features to detect fraud. We conclude that (1) complex methods do not necessarily outperform basic network features, and that (2) network analytics helps to detect different fraud patterns, compared to models trained on claim-specific features alone. [ABSTRACT FROM AUTHOR]

Abstract In this work, we explore the extent to which the spectrum of the graph Laplacian can characterize the probability distribution of random graphs for the purpose of model evaluation and model selection for network data applications. Network data, often represented as a graph, consist of a set of pairwise observations between elements of a population of interests. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including stochastic block models, latent node position models, and exponential families of random graph models. We develop a novel methodology which exploits the information contained in the spectrum of the graph Laplacian to predict the data-generating model from a set of candidate models. Through simulation studies, we explore the extent to which network data models can be differentiated by the spectrum of the graph Laplacian. We demonstrate the potential of our method through two applications to well-studied network data sets and validate our findings against existing analyses in the statistical network analysis literature.

Networks consist of interconnected units, known as nodes, and allow to formally describe interactions within a system. Specifically, bipartite networks depict relationships between two distinct sets of nodes, designated as sending and receiving nodes. An integral aspect of bipartite network analysis often involves identifying clusters of nodes with similar behaviors. The computational complexity of models for large bipartite networks poses a challenge. To mitigate this challenge, we employ a Mixture of Latent Trait Analyzers (MLTA) for node clustering. Our approach extends the MLTA to include covariates and introduces a double EM algorithm for estimation. Applying our method to COVID-19 data, with sending nodes representing patients and receiving nodes representing preventive measures, enables dimensionality reduction and the identification of meaningful groups. We present simulation results demonstrating the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

The latent position model (LPM) is a popular method used in network data analysis where nodes are assumed to be positioned in a p$$ p $$‐dimensional latent space. The latent shrinkage position model (LSPM) is an extension of the LPM which automatically determines the number of effective dimensions of the latent space via a Bayesian nonparametric shrinkage prior. However, the LSPM's reliance on Markov chain Monte Carlo for inference, while rigorous, is computationally expensive, making it challenging to scale to networks with large numbers of nodes. We introduce a variational inference approach for the LSPM, aiming to reduce computational demands while retaining the model's ability to intrinsically determine the number of effective latent dimensions. The performance of the variational LSPM is illustrated through simulation studies and its application to real‐world network data. To promote wider adoption and ease of implementation, we also provide open‐source code. [ABSTRACT FROM AUTHOR]

A hospital operating status evaluation data analysis system was established based on the autoencoder's network. The Gibbs sampling method is used to obtain the approximate distribution of RBM. In addition, the Autoencoder neural network can also select feature dimensions that can better characterize the characteristics of financial operation data from a large amount of financial operation data. Deep learning methods are used to study the redundant information elimination method and the generation mechanism of multi-source heterogeneity in multi-source heterogeneous networks. The principle of intrinsic compression is used to reduce the dimensionality of the redundancy in the network and obtain the compression redundancy objective function. This article sets thresholds for information classification on the Internet. The approach was tested using financial data from a medical institution. Use smart encoders to extract 17 financial indicators from financial data that can be used for modeling. The evaluation results are used as the output vector of the model. Comparative experiments show that the AUC value and accuracy of the method proposed in this article can be improved by 0.84 and 83.33% compared with the AUC value of shallow logistic regression and BP neural network. This algorithm has apparent improvements. [ABSTRACT FROM AUTHOR]

Networks (graphs) permeate scientific fields such as biology, social science, economics, etc. Empirical studies have shown that real-world networks are often heterogeneous, that is, the degrees of nodes do not concentrate on a number. Recently, the Rényi index was tentatively used to measure network heterogeneity. However, the validity of the Rényi index in network settings is not theoretically justified. In this paper, we study this problem. We derive the limit of the Rényi index of a heterogeneous Erdös–Rényi random graph and a power-law random graph, as well as the convergence rates. Our results show that the Erdös–Rényi random graph has asymptotic Rényi index zero and the power-law random graph (highly heterogeneous) has asymptotic Rényi index one. In addition, the limit of the Rényi index increases as the graph gets more heterogeneous. These results theoretically justify the Rényi index is a reasonable statistical measure of network heterogeneity. We also evaluate the finite-sample performance of the Rényi index by simulation. [ABSTRACT FROM AUTHOR]

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Statistical analysis for populations of networks is widely applicable, but challenging, as networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework for studying populations of unlabelled networks that are weighted or unweighted, uni- or multilayered, directed or undirected. Viewing graph space as the quotient of a Euclidean space with respect to a finite group action, we show that it is not a manifold, and that its curvature is unbounded from above. Within this geometrical framework we define generalized geodesic principal components, and we introduce the align-all-and-compute algorithms, all of which allow for the computation of statistics on graph space. The statistics and algorithms are compared with existing methods and empirically validated on three real datasets, showcasing the potential utility of the framework. The whole framework is implemented within the geomstats Python package. [ABSTRACT FROM AUTHOR]

Due to the increasing severity of network security issues, training corresponding detection models requires large datasets. In this work, we propose a novel method based on generative adversarial networks to synthesize network data traffic. We introduced a network traffic data normalization method based on Gaussian mixture models (GMM), and for the first time, incorporated a generator based on the Swin Transformer structure into the field of network traffic generation. To further enhance the robustness of the model, we mapped real data through an AE (autoencoder) module and optimized the training results in the form of evolutionary algorithms. We validated the training results on four different datasets and introduced four additional models for comparative experiments in the experimental evaluation section. Our proposed SEGAN outperformed other state-of-the-art network traffic emulation methods. [ABSTRACT FROM AUTHOR]

The use of unsupervised machine learning models for anomaly detection is a common thing nowadays. While many research papers focus on improving and testing these models, there is a lack of those that deal with threshold selection, which is an important step in implementing a good anomaly detection system. In this paper, we investigate different supervised and unsupervised threshold selection methods found in the network anomaly detection literature. A total of five supervised and twenty unsupervised methods were found, all of which are described, categorized, and implemented in this paper. The unsupervised methods were further categorized according to the input data they expect, the type of output data they produce, and whether they are parametric or not, and divided into six groups according to the idea behind these methods: Statistics-based, Distribution-based, Clustering-based, Density-based, Graphical-based methods and Other. To test all the methods found, two different testing scenarios are created. The first one focuses on using data with anomalies and the second one uses only the normal data. Based on these two scenarios, tests were performed with real firewall log data containing three types of injected anomalies. The results are presented in the form of boxplots of the Matthews correlation coefficient for nine datasets. To draw a conclusion, both the method groups and the individual methods were compared in terms of evaluation metrics and execution times as well as in comparison to the methods already implemented in the PyThresh toolkit.

In this paper, we study the impact of combining profile and network data in solving record de-duplication problems. We also assess the influence of a range of prior distributions on the linkage structure, and explore the use of stochastic gradient Hamiltonian Monte Carlo methods as a faster alternative to obtain samples from the posterior distribution for network parameters. Our methodology is evaluated using the RLdata500 data, which is a popular dataset in the record linkage literature. [ABSTRACT FROM AUTHOR]

Artificial immune detection can be used to detect network intrusions in an adaptive approach and proper matching methods can improve the accuracy of immune detection methods. This paper proposes an artificial immune detection model for network intrusion data based on a quantitative matching method. The proposed model defines the detection process by using network data and decimal values to express features and artificial immune mechanisms are simulated to define immune elements. Then, to improve the accuracy of similarity calculation, a quantitative matching method is proposed. The model uses mathematical methods to train and evolve immune elements, increasing the diversity of immune recognition and allowing for the successful detection of unknown intrusions. The proposed model's objective is to accurately identify known intrusions and expand the identification of unknown intrusions through signature detection and immune detection, overcoming the disadvantages of traditional methods. The experiment results show that the proposed model can detect intrusions effectively. It has a detection rate of more than 99.6% on average and a false alarm rate of 0.0264%. It outperforms existing immune intrusion detection methods in terms of comprehensive detection performance. [ABSTRACT FROM AUTHOR]

Currently conventional intrusion detection methods for digital campus networks mainly batch process the data by constructing a autoencoder and construct a detection criterion by learning the data features of malicious attacks, which leads to poor detection accuracy due to neglecting the offsets of different data sources. In this regard, An IoT intrusion detection method for digital campus network based on feature fusion of offset data in multi - source domain was proposed. Firstly, the feature dimension was judged, so as to clarify the type of data that can be extracted. Then by constructing the offset coefficient correction index, the offset data from multi - source domain was fused and processed, and the optimization iteration was used to optimize the feature parameters at different levels. Finally, the feature offset criteria are extracted, and the fused feature vectors were compared with the offset criteria to realize the effective judgment of the intrusion data. The experimental results show that, the proposed method has higher detection accuracy and better detection effect detection effect. [ABSTRACT FROM AUTHOR]

Vector autoregression model is ubiquitous in classical time series data analysis. With the rapid advance of social network sites, time series data over latent graph is becoming increasingly popular. In this article, we develop a novel Bayesian grouped network autoregression model, which can simultaneously estimate group information (number of groups and group configurations) and group-wise parameters. Specifically, a graphically assisted Chinese restaurant process is incorporated under the framework of the network autoregression model to improve the statistical inference performance. An efficient Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. Extensive studies are conducted to evaluate the finite sample performance of our proposed methodology. Additionally, we analyze two real datasets as illustrations of the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently aggregate signal across different layers, we argue that the sum-of-squared adjacency matrices contain sufficient signal even when individual layers are very sparse. Our method uses a bias-removal step that is necessary when the squared noise matrices may overwhelm the signal in the very sparse regime. The analysis of our method relies on several novel tail probability bounds for matrix linear combinations with matrix-valued coefficients and matrix-valued quadratic forms, which may be of independent interest. The performance of our method and the necessity of bias removal is demonstrated in synthetic data and in microarray analysis about gene co-expression networks. for this article are available online. [ABSTRACT FROM AUTHOR]

In order to improve data security and network data security in the digital economy-driven environment, this paper combines data security technology and network security technology to build a digital economy security management and control system. Moreover, this paper describes the data encryption of the data owners before the framework index and the composition and construction method of the corresponding EncIR tree, and analyzes the spatial keyword group query algorithm on the EncIR tree. In addition, this paper analyzes the experimental performance of index building and spatial query, and builds an intelligent digital economy security system on the basis of these algorithms. The experimental research results verify that the data security technology and network data system driven by the digital economy have good security performance, and on this basis, follow-up security regulations can be formulated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we introduce a novel Bayesian approach for linking multiple social networks in order to discover the same real world person having different accounts across networks. In particular, we develop a latent model that allows us to jointly characterize the network and linkage structures relying on both relational and profile data. In contrast to other existing approaches in the machine learning literature, our Bayesian implementation naturally provides uncertainty quantification via posterior probabilities for the linkage structure itself or any function of it. Our findings clearly suggest that our methodology can produce accurate point estimates of the linkage structure even in the absence of profile information, and also, in an identity resolution setting, our results confirm that including relational data into the matching process improves the linkage accuracy. We illustrate our methodology using real data from popular social networks such as Twitter, Facebook, and YouTube. [ABSTRACT FROM AUTHOR]

We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over the rectangles and subsequently develop novel multiplier bootstraps with theoretical guarantees. These theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We exhibit applications of our methods to uniform confidence bands for density estimation under joint exchangeability and penalty choice for l 1 -penalized regression under separate exchangeability. Extensive simulations demonstrate precise uniform coverage rates. We illustrate by constructing uniform confidence bands for international trade network densities. [ABSTRACT FROM AUTHOR]

Due to the increasing severity of network security issues, training corresponding detection models requires large datasets. In this work, we propose a novel method based on generative adversarial networks to synthesize network data traffic. We introduced a network traffic data normalization method based on Gaussian mixture models (GMM), and for the first time, incorporated a generator based on the Swin Transformer structure into the field of network traffic generation. To further enhance the robustness of the model, we mapped real data through an AE (autoencoder) module and optimized the training results in the form of evolutionary algorithms. We validated the training results on four different datasets and introduced four additional models for comparative experiments in the experimental evaluation section. Our proposed SEGAN outperformed other state-of-the-art network traffic emulation methods.

The asymptotic normality of a fixed number of the maximum likelihood estimators in a directed network model with degree heterogeneity and homophily has been established recently. In this article, we further derive a central limit theorem for a linear combination of all the maximum likelihood estimators of degree parameter when the number of nodes goes to infinity. Simulation studies are provided to illustrate the asymptotic results. [ABSTRACT FROM AUTHOR]

To ensure the security of network data transmission, a network data encryption method based on TrustZone was analyzed. The hardware layer was used to provide hardware support for network data encryption. The framework layer was provided with a trusted operating kernel and a common kernel with a rich execution environment through the kernel layer. The framework layer used the key security management unit on the client-application-side to create, write, read, and delete the security key file. The network data encryption and decryption unit on the client-application-side constructed a session connection between the client application side and the trusted application side under the kernel provided by the kernel layer by calling the hardware of the hardware layer. Moreover, the network data encryption and decryption instructions were transmitted to the trusted-application-side network data encryption and decryption unit. The encryption of the memristor neural network and the cubic chaotic map were employed. The network data encryption and decryption results were presented to the user through the application layer. Experiments results prove that, the interval of the optimal key chaotic sequence must be controlled between [-1,1]. The ASCII code value of the network data character sequence before encryption has an obvious distribution pattern to encrypt the network data to be transmitted under the wireless sensor network scenario. The value of the 0-1 balance index of the encrypted network data of this study's method is the closest to 0, and the highest values are approximately 0.0088, 0.0079, and 0.0067. The method in this study can effectively encrypt and decrypt network data. Under different attack types, this method has high integrity of encrypted network data and a high value of avalanche effect. Thus, it has effective anti-attack performance. [ABSTRACT FROM AUTHOR]

It has become an increasingly common practice in modern science and engineering to collect samples of multiple network data in which a network serves as a basic data object. The increasing prevalence of multiple network data calls for developments of models and theories that can deal with inference problems for populations of networks. In this work, we propose a general procedure for hypothesis testing of networks and in particular, for differentiating distributions of two samples of networks. We consider a very general framework which allows us to perform test on large and sparse networks. Our contribution is two-fold: (1) We propose a test statistics based on the singular value of a generalized Wigner matrix. The asymptotic null distribution of the statistics is shown to follow the Tracy–Widom distribution as the number of nodes tends to infinity. The test also yields asymptotic power guarantee with the power tending to one under the alternative; (2) The test procedure is adapted for change-point detection in dynamic networks which is proven to be consistent in detecting the change-points. In addition to theoretical guarantees, another appealing feature of this adapted procedure is that it provides a principled and simple method for selecting the threshold that is also allowed to vary with time. Extensive simulation studies and real data analyses demonstrate the superior performance of our procedure with competitors. [ABSTRACT FROM AUTHOR]

Continuing education platforms are faced with problems such as the aging of online learning platforms and backward technology. The data center network is an essential infrastructure supporting the big data and cloud computing platform continuing education network. It is widely used for data-intensive and massively parallel computing tasks. The paper proposes a continuing education network data center management model based on this research background. At the same time, this paper proposes a real-time encryption method for distributed data in a multi-layer differential continuing education network based on fractional differential mathematical equations. The experimental study found that the fractional differential mathematical equations method can effectively control the stability of data transmission of continuing education receipt networks. This algorithm improves the efficiency of network data operation and controls the cost of encryption. The research results of this paper provide technical support for network education.

Abstract The deluge of network datasets demands a standard way to effectively and succinctly summarize network datasets. Building on similar efforts to standardize the documentation of models and datasets in machine learning, here we propose network cards, short summaries of network datasets that can capture not only the basic statistics of the network but also information about the data construction process, provenance, ethical considerations, and other metadata. In this paper, we lay out (1) the rationales and objectives for network cards, (2) key elements that should be included in network cards, and (3) example network cards to underscore their benefits across a variety of research domains. We also provide a schema, templates, and a software package for generating network cards.

Federated Learning (FL) is a newly emerged federated optimization technique for distributed data in a federated network. The participants in FL that train the model locally are classified into client nodes. The server node assumes the responsibility to aggregate local models from client nodes without data moving. In this regard, FL is an ideal solution to protect data privacy at each node of the network. However, the raw data generated on each node are unlabeled, making it impossible for FL to apply these data directly to train a model. The large volume of data annotating work prevents FL from being widely applied in the real world, especially for online scenarios, where the data are generated continuously. Meanwhile, the data generated on different nodes tend to be differently distributed. It has been proved theoretically and experimentally that non-independent and identically distributed (non-IID) data harm the performance of FL. In this article, we design a semi-federated active learning (semi-FAL) framework to tackle the annotation and non-IID problems jointly. More specifically, the server node can provide (i) a pre-trained model to help each client node annotate the local data uniformly and (ii) an estimation of the global gradient to help correct the local gradient. The evaluation results demonstrate our semi-FAL framework can efficiently handle unlabeled online network data and achieves high accuracy and fast convergence. [ABSTRACT FROM AUTHOR]

Networks are widely used to describe relational data among objects in a complex system. As network data often exhibit clustering structures, research interest often focuses on discovering clusters of nodes. We develop a novel concordance-based method for node clustering in networks, where a linear model is imposed on the latent position of each node with respect to a node-specific center and its covariates via linear transformation. By maximizing a triangular concordance function with a concave pairwise penalty, the latent positions are estimated so that each node would be more likely to be close to its neighbors in contrast to non-neighbors and nodes are clustered by their node-specific centers. We develop an alternating direction method of multipliers algorithm for parameter estimation and an intimacy score between unlinked nodes for link prediction. Our method takes into account common characteristics of network data (i.e., assortativity, link pattern similarity, node heterogeneity and link transitivity), while it does not require the number of clusters to be known. The clustering effectiveness and link prediction accuracy of our method are demonstrated in simulated and real networks. for this article are available online. [ABSTRACT FROM AUTHOR]

Samples often are collected by a network in many modern applications, and the network structure information is potentially helpful in making regression predictions. However, most regression models assume the samples are independent, such as Lasso. Motivated by this, taking the network information into account, we propose a Network Lasso model for regression prediction in this paper. Specially, we consider the effect of the neighborhoods to each response and model each yi as a linear combination of the covariates xi, the connected neighbors yj, and an error term ϵi. The corresponding coefficients are referred to effect of node and neighborhoods, respectively. The consistency of the estimators are also established under the regimes where the neighborhoods effect coefficients are known and unknown, respectively. Finally, we evaluate the performance of the proposed model through a series of simulations and a latitude data example. [ABSTRACT FROM AUTHOR]

We present acreg, a new command that implements the arbitrary clustering correction of standard errors proposed in Colella et al. (2019, IZA discussion paper 12584). Arbitrary here refers to the way observational units are correlated with each other: we impose no restrictions so that our approach can be used with a wide range of data. The command accommodates both cross-sectional and panel databases and allows the estimation of ordinary least-squares and two-stage least-squares coefficients, correcting standard errors in three environments: in a spatial setting using units' coordinates or distance between units, in a network setting starting from the adjacency matrix, and in a multiway clustering framework taking multiple clustering variables as input. Distance and time cutoffs can be specified by the user, and linear decays in time and space are also optional. [ABSTRACT FROM AUTHOR]

The use of network analysis to understand relationships among actors and organizations in coordinated actions has grown in recent years. Examining the network structure and functions in disaster response has gained particular attention. Different methods of data collection and analysis are utilized in network research. The use of documents as a data source has also gained traction. Scholars utilize content analysis of documents to uncover network structure, i.e., core "nodes," and functions. This is especially critical in emergency and crisis management as the associated network involves complex set of actors from different sectors and jurisdictions, and first-hand recollections of representatives might not be inclusive of every interaction and specific actors they worked with. With augmented utilization, there is a need to understand the methodological process of document use as a primary means of data analysis in emergency management. This study fills that gap by providing a systematic literature review of empirical studies across a broad range of subjects that have discussed document collection and use for network analysis. Furthermore, this study provides a detailed example of the method of document identification and collection, data generation and organization process, and network visualization and analysis in an emergency and crisis management context. The study concludes with answering, for disaster response networks, what types of documentary data are utilized and how they are used, the types of disasters that have been prevalent in utilizing this method, and the process undertaken to analyze and visualize networks. [ABSTRACT FROM AUTHOR]

Abstract.For differential privacy under sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this article, we release the degree sequences of the binary networks under a general noisy mechanism, with the discrete Laplace mechanism as a special case. We establish the asymptotic result, including both consistency and asymptotically normality, of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real-data example are provided to illustrate the asymptotic results. [ABSTRACT FROM AUTHOR]

Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies of functionalities and evolution patterns of complex networks. To elucidate the role of higher-order structures in community detection over networks, we introduce a Superimposed Stochastic Block Model (SupSBM). The model is based on a random graph framework in which certain higher-order structures or subgraphs are generated through an independent hyperedge generation process and then replaced with graphs superimposed with edges generated by an inhomogeneous random graph model. Consequently, the model introduces dependencies between edges which allow for capturing more realistic network phenomena, namely strong local clustering in a sparse network, short average path length, and community structure. We then proceed to rigorously analyze the performance of a recently proposed higher-order spectral clustering method on the SupSBM. In particular, we prove non-asymptotic upper bounds on the misclustering error of higher-order spectral community detection for a SupSBM setting in which triangles are superimposed with undirected edges. We assess the model fit of the proposed model and compare it with existing random graph models in terms of observed properties of real network data obtained from diverse domains by sampling networks from the fitted models and a nonparametric network cross-validation approach. [ABSTRACT FROM AUTHOR]

The stochastic block model (SBM) and its variants constitute an important family of probabilistic tools for studying network data. There is a rich literature on methods for estimating block labels and model parameters of stochastic block models. Most of these studies require the number of communities K as an input, making the estimation of K an important problem. Cross-validation is a natural option for this problem since it is a widely used generic method for evaluating model fitting. However, crossvalidation is known to be inconsistent and prone to overfitting unless impractical split ratios are used. Cross-validation with confidence (CVC) is proposed with better theoretical guarantees in conventional settings. We study the properties of CVC for stochastic block models. Our theoretical studies show that CVC, unlike the standard cross-validation, can consistently pick the optimal K under suitable conditions. We implement this method and check its performance against other established methods on both synthetic and real datasets. [ABSTRACT FROM AUTHOR]