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非均匀高维稀疏多重超图的通用潜在嵌入建模AI 解读

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations, including their heavy reliance on uniformity restrictions for hyperlink orders and their inability to account for repeated observations of identical hyperlinks. In this work, we introduce a novel and general latent embedding approach that…

固定与增长数量的尖峰特征值：极限规律和一致估计准则AI 解读

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension p with the number of spikes k. Allowing both p and k to diverge, we derive limiting distributions of the spiked sample eigenvalues using random matrix theory techniques. Notably, our results are established under a general spiked covariance model, where the bulk eigenvalues are allowed to differ, and the spiked eigenvalues need not be…

曲率可学习的双曲网络潜在空间模型AI 解读

Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a significant, unresolved issue. In this work, we propose a hyperbolic network latent space model with a learnable curvature parameter. We theoretically justify that learning the optimal curvature is essential to minimizing the embedding error…

网络关联数据的高维因子分析AI 解读

Summary Factor analysis is a statistical tool widely used in many disciplines, such as psychology, economics and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor analysis is an important problem that remains open. This article focuses on high-dimensional factor analysis involving network-connected observations, and we propose a generalized factor model with latent factors that account for both the network…

维度递增随机图模型中的似然比检验AI 解读

We explore the Wilks phenomena in two random graph models: the β-model and the Bradley–Terry model. For two increasing dimensional null hypotheses, including a specified null H0:βi=βi0 for i=1,…,r and a homogenous null H0:β1=⋯=βr, we reveal high dimensional Wilks’ phenomena that the normalized log-likelihood ratio statistic, [2{l(β̂)−l(β̂0)}−r]/(2r)1/2, converges in distribution to the standard normal distribution as r goes to infinity. Here, l(β) is the log-likelihood…

兼顾多样性与异质受欢迎程度的超图建模AI 解读

While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, that is, those between two individuals.This article addresses the less studied, though commonly encountered, polyadic relations that can involve more than two individuals.In particular, we propose a new latent space model for hypergraphs using determinantal point processes,…

网络辅助回归的保形预测AI 解读

An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics. While standard regression methods that make use of both types of covariates may be used for prediction, statistical inference is complicated by the fact that the nodal summary statistics are often dependent in complex ways. We show that under…

符号网络的总体层面平衡AI 解读

Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for signed networks have been largely unexplored. In signed networks, there exist both positive (e.g., like, trust) and negative (e.g., dislike, distrust) edges, which are commonly seen in real-world scenarios. The positive and negative edges in signed networks lead to unique structural patterns, which pose challenges…

基于常微分方程的生存分析AI 解读

This article introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable, and easy-to-implement procedure for estimation and inference. Specifically, the ODE modeling framework unifies many existing survival models, such as the proportional hazards model, the linear transformation model, the accelerated…

基于剖面伪似然的快速网络社区检测AI 解读

The stochastic block model is one of the most studied network models for community detection, and fitting its likelihood function on large-scale networks is known to be challenging. One prominent work that overcomes this computational challenge is the fast pseudo-likelihood approach proposed by Amini et al. for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and may not be well suited for small and medium…

结合高维节点变量的网络联合潜在空间模型AI 解读

Summary Network latent space models assume that each node is associated with an unobserved latent position in a Euclidean , and such latent variables determine the probability of two nodes connecting with each other. In many applications, nodes in the network are often observed along with high-dimensional node variables, and these node variables provide important information for understanding the network structure. However, classical network latent space models have several…

脑电脑机接口中神经活动的贝叶斯推断AI 解读

A brain-computer interface (BCI) is a system that translates brain activity into commands to operate technology. A common design for an electroencephalogram (EEG) BCI relies on the classification of the P300 event-related potential (ERP), which is a response elicited by the rare occurrence of target stimuli among common non-target stimuli. Few existing ERP classifiers directly explore the underlying mechanism of the neural activity. To this end, we perform a novel Bayesian…

利用最大逐元素偏差检验随机区块模型的拟合优度AI 解读

–The stochastic block model is widely used for detecting community structures in network data. How to test the goodness of fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article, we propose a novel goodness-of-fit test based on the maximum entry of the centered and rescaled adjacency matrix for the stochastic block model. One noticeable advantage of the proposed test is that the number of communities can be…

《基于边抽样的网络交叉验证》讨论回复AI 解读

We thank the editor for organizing this discussion and giving us the opportunity to read experts’ perspectives on our work. We are grateful to all the discussants for their insightful contributions, which raise many important points and offer suggestions for potential improvements and generalizations of our method. In this rejoinder we provide some clarifications, remarks and selected numerical results in response to these comments. Lei & Lin (2020) conjecture, and we agree,…

通过边抽样进行网络交叉验证AI 解读

Summary While many statistical models and methods are now available for network analysis, resampling of network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but it is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. In this paper we propose a new network resampling strategy, based on splitting node pairs…

通过邻域平滑估计网络连边概率AI 解读

Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the…

双度序列维度增长的有向指数随机图模型渐近理论AI 解读

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and…

度数修正随机区块模型下网络社区检测的一致性AI 解读

Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of community detection under the block model have been recently developed. However, the block model is limited by its assumption that all nodes within a community are stochastically equivalent, and provides a poor fit to networks with hubs or…

具有强遗传约束的变量选择及其预言性质AI 解读

In this paper, we extend the LASSO method (Tibshirani 1996) for simultaneously fitting a regression model and identifying important interaction terms. Unlike most of the existing variable selection methods, our method automatically enforces the heredity constraint, that is, an interaction term can be included in the model only if the corresponding main terms are also included in the model. Furthermore, we extend our method to generalized linear models, and show that it…

可解释的函数型线性回归AI 解读

Regression models to relate a scalar Y to a functional predictor X(t) are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, β(t), with Y related to X(t) through ∫β(t)X(t) dt. Regions where β(t)≠0 correspond to places where there is a relationship between X(t) and Y. Alternatively, points where β(t)=0 indicate no relationship. Hence, for interpretation purposes, it is desirable for a regression procedure to be capable of…

利用联合稀疏回归模型估计偏相关AI 解读

In this paper, we propose a computationally efficient approach -space(Sparse PArtial Correlation Estimation)- for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial…

大型协方差矩阵的广义阈值化AI 解读

We propose a new class of generalized thresholding operators that combine thresholding with shrinkage, and study generalized thresholding of the sample covariance matrix in high dimensions. Generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden. We obtain an explicit convergence rate in the operator norm that shows the tradeoff between the sparsity of the true model, dimension, and the sample size, and…

再生核希尔伯特空间中的分位数回归AI 解读

In this article we consider quantile regression in reproducing kernel Hilbert spaces, which we call kernel quantile regression (KQR). We make three contributions: (1) we propose an efficient algorithm that computes the entire solution path of the KQR, with essentially the same computational cost as fitting one KQR model; (2) we derive a simple formula for the effective dimension of the KQR model, which allows convenient selection of the regularization parameter; and (3) we…

通过融合 Lasso 实现稀疏性与平滑性AI 解读

Summary The lasso penalizes a least squares regression by the sum of the absolute values (L1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients equal to 0). We propose the ‘fused lasso’, a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the L1-norm of both the coefficients and their successive differences. Thus it encourages sparsity of the…