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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…

高维矩阵因子模型的准最大似然估计AI 解读

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator…

高维矩阵值序列的建模与学习AI 解读

We propose a new matrix factor model, named RaDFaM, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. RaDFaM contributes a novel class of low-rank latent structure that makes tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued…

高维矩阵值时间序列的双向动态因子模型AI 解读

Abstract In this article, we introduce a two-way dynamic factor model (2w-DFM) for high-dimensional matrix-valued time series and study some of the basic theoretical properties in terms of identifiability and estimation accuracy. The proposed model aims to capture separable and low-dimensional effects of row and column attributes and their correlations across rows, columns, and time points. Complementary to other dynamic factor models for high-dimensional data, the 2w-DFM…

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…

通过调整特征值阈值估计因子数量AI 解读

Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the eigenvalues of the covariance matrix caused by heterogeneous scales of observed variables, it is very difficult to give an accurate relationship between these eigenvalues and the number of common factors. To overcome this limitation, we appeal to…

高维相关矩阵检验AI 解读

Testing correlation structures has attracted extensive attention in the literature due to both its importance in real applications and several major theoretical challenges. The aim of this paper is to develop a general framework of testing correlation structures for the one-, two-, and multiple sample testing problems under a high-dimensional setting when both the sample size and data dimension go to infinity. Our test statistics are designed to deal with both the dense and…

高维线性回归中的样条 LassoAI 解读

We consider a high-dimensional linear regression problem, where the covariates (features) are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. The fused lasso of Tibshirani et al. is designed especially to tackle this type of problems; it yields sparse coefficients and selects grouped variables, and encourages local constant coefficient profile within each group. However, in some applications, the effects of different…

多样本混合模型的似然比检验及其基因印记应用AI 解读

Genomic imprinting is a known aspect of the etiology of many diseases. The imprinting phenomenon depicts differential expression levels of the allele depending on its parental origin. When the parental origin is unknown, the expression level has a finite normal mixture distribution. In such applications, a random sample of expression levels consists of three subsamples according to the number of minor alleles an individual possesses, of which one is the mixture and the other…

时变朴素贝叶斯模型及其在中文文本分类中的应用AI 解读

Document classification is an area of great importance for which many classification methods have been developed. However, most of these methods cannot generate time-dependent classification rules. Thus, they are not the best choices for problems with time-varying structures. To address this problem, we propose a varying naïve Bayes model, which is a natural extension of the naïve Bayes model that allows for time-dependent classification rule. The method of kernel smoothing…

流行病学研究中的混杂因素判定标准AI 解读

Summary The paper addresses a formal definition of a confounder based on the qualitative definition that is commonly used in standard epidemiology text-books. To derive the criterion for a factor to be a confounder given by Miettinen and Cook and to clarify inconsistency between various criteria for a confounder, we introduce the concepts of an irrelevant factor, an occasional confounder and a uniformly irrelevant factor. We discuss criteria for checking these and show that…

Logistic 回归系数的可折叠性AI 解读

SUMMARY In this paper we discuss collapsibility of logistic regression coefficients over a background variable and present necessary and sufficient conditions for collapsibility.