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动态网络模型与图函数估计AI 解读

In the present paper, we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities $\mathbf{{\Lambda}}$ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In particular, in the context of the DSBM, we derive a penalized least squares estimator $\widehat{\boldsymbol{\Lambda}}$ of $\mathbf{{\Lambda}}$ and show that $\widehat{\boldsymbol{\Lambda}}$ satisfies an oracle inequality and also…

贝叶斯 Probit 回归中 Albert–Chib 算法的收敛复杂度分析AI 解读

The use of MCMC algorithms in high dimensional Bayesian problems has become routine. This has spurred so-called convergence complexity analysis, the goal of which is to ascertain how the convergence rate of a Monte Carlo Markov chain scales with sample size, $n$, and/or number of covariates, $p$. This article provides a thorough convergence complexity analysis of Albert and Chib’s [J. Amer. Statist. Assoc. 88 (1993) 669–679] data augmentation algorithm for the Bayesian…

深度学习缓解非参数回归维数灾难的理论研究AI 解读

Assuming that a smoothness condition and a suitable restriction on the structure of the regression function hold, it is shown that least squares estimates based on multilayer feedforward neural networks are able to circumvent the curse of dimensionality in nonparametric regression. The proof is based on new approximation results concerning multilayer feedforward neural networks with bounded weights and a bounded number of hidden neurons. The estimates are compared with…

谱方法与正则化极大似然均可实现最优前 K 项排序AI 解读

This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model—the Bradley–Terry–Luce model, where each item is assigned a latent preference score, and where the outcome of each pairwise comparison depends solely on the relative scores of…

稀疏备择下的高维变点检测AI 解读

We consider the problem of detecting a change in mean in a sequence of high-dimensional Gaussian vectors. The change in mean may be occurring simultaneously in an unknown subset components. We propose a hypothesis test to detect the presence of a change-point and establish the detection boundary in different regimes under the assumption that the dimension tends to infinity and the length of the sequence grows with the dimension. A remarkable feature of the proposed test is…

使用高频数据检验因子数量的秩检验AI 解读

In the literature, consistency of the estimates of the number of factors for large-dimensional factor models had been extensively studied recently. But the second-order property of the estimator has long been unsolved due to lack of limiting distribution of the estimators. In this paper, we propose a rank test of the number of factors using large panel high-frequency data contaminated with microstructure noise. The rank test is realized by forming a fixed number of…

尾部的故事：高维尾部相依性AI 解读

Summary We propose a simple and flexible framework that allows for a comprehensive analysis of tail interdependence in high dimensions. We use co‐exceedances to capture the structure of the dependence in the tails and, relying on the concept of multi‐information, define the coefficient of tail interdependence. Within this framework, we develop statistical tests of (i) independence in the tails, (ii) goodness‐of‐fit of the tail interdependence structure of a hypothesized…

大规模数据中回归系数的空间同质性识别AI 解读

Spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest, taking into account the spatial dependence of the observations. In many applications, relationships between response variables and covariates are expected to exhibit complex spatial patterns. We propose a new approach, referred to as spatially clustered coefficient (SCC) regression, to detect spatially clustered…

利用机器学习估计和检验疫苗筛效应AI 解读

When available, vaccines are an effective means of disease prevention. Unfortunately, efficacious vaccines have not yet been developed for several major infectious diseases, including HIV and malaria. Vaccine sieve analysis studies whether and how the efficacy of a vaccine varies with the genetics of the pathogen of interest, which can guide subsequent vaccine development and deployment. In sieve analyses, the effect of the vaccine on the cumulative incidence corresponding…

从脑电读数样本推断脑信号同步性AI 解读

Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is intuitively and statistically appealing to rely on readings from more than one individual in order to highlight recurrent patterns of brain activation, pooling information across subjects presents non-trivial methodological problems. We discuss some of the scientific issues associated with the…

多表型研究中主成分关联检验功效的几何视角AI 解读

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high dimensional, has been proposed to analyze multiple correlated phenotypes. It has been empirically observed that the first PC, which summarizes the largest amount of variance, can be less powerful than higher-order PCs and other commonly used methods in…

存在部分无效工具变量时Lasso在工具变量估计中的使用AI 解读

We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator…

高通量检测中区域识别的选择校正统计推断AI 解读

Scientists use high-dimensional measurement assays to detect and prioritize regions of strong signal in spatially organized domain. Examples include finding methylation enriched genomic regions using microarrays, and active cortical areas using brain-imaging. The most common procedure for detecting potential regions is to group neighboring sites where the signal passed a threshold. However, one needs to account for the selection bias induced by this procedure to avoid…

Dynamic treatment regimes are a set of decision rules and each treatment decision is tailored over time according to patients' responses to previous treatments as well as covariate history. There is a growing interest in development of correct statistical inference for optimal dynamic treatment regimes to handle the challenges of non-regularity problems in the presence of non-respondents who have zero-treatment effects, especially when the dimension of the tailoring…

高维协变量调整的张量分类AI 解读

In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor (i.e., multi-dimensional array) and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called the CATCH model (short for covariate-adjusted tensor classification in high-dimensions). The CATCH model efficiently integrates the covariates and…

超高维充分降维与同步变量选择的稀疏最小差异方法AI 解读

Sufficient dimension reduction (SDR) is known to be a powerful tool for achieving data reduction and data visualization in regression and classification problems. In this work, we study ultrahigh-dimensional SDR problems and propose solutions under a unified minimum discrepancy approach with regularization. When p grows exponentially with n, consistency results in both central subspace estimation and variable selection are established simultaneously for important SDR…

具有差异化收缩的图模型贝叶斯正则化AI 解读

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new nonconvex penalty approximating the ℓ0 penalty. Optimal error rates for estimation consistency in terms of various…

Skinny Gibbs：一致且可扩展的模型选择 Gibbs 采样器AI 解读

Naveen N. Narisettya, Juan Shenb* & Xuming Heca Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, ILb Department of Statistics, Fudan University, Shanghai, Chinac Department of Statistics, University of Michigan, Ann Arbor, MICONTACT Juan Shen shenjuan@fudan.edu.cn Department of Statistics, Fudan University, Shanghai, ChinaColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary…

因子成分与特异成分的经验过程AI 解读

The distributions of the common and idiosyncratic components for an individual variable are important in forecasting and applications. However, they are not identified with low-dimensional observations. Using the recently developed theory for large dimensional approximate factor model for large panel data, the common and idiosyncratic components can be estimated consistently. Based on the estimated common and idiosyncratic components, we construct the empirical processes for…

分位数回归模型的失拟检验AI 解读

Summary The paper novelly transforms lack-of-fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two-sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test…

可扩展的重要性调温与贝叶斯变量选择AI 解读

Summary We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to…

存在部分隐藏变量时的稳健因果结构学习AI 解读

Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables and then…

通过广义信赖推断进行高维线性模型的非惩罚变量选择AI 解读

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge, an entirely new perspective on variable selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies…

Wiener 泛函最大值的高斯近似及高频数据应用AI 解读

This paper establishes an upper bound for the Kolmogorov distance between the maximum of a high-dimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As a special case, we show that the maximum of multiple Wiener–Itô integrals with common orders is well approximated by its Gaussian analog in terms of the Kolmogorov distance if their covariance matrices are close to each other and the maximum of the fourth cumulants of the multiple…