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超高维稀疏数据中基于条件严格凸损失的非参数筛选AI 解读

Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality $p$ and the sample size $n$ can satisfy the NP dimensionality $\log p=O(n^{a})$ for some $a>0$ [J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 (2008) 849–911]. The current paper aims to simultaneously tackle the “universality” and “effectiveness” of sure screening procedures. For the “universality,” we develop a general and…

全正性约束下高斯模型的最大似然估计AI 解读

We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_{2}$). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof that the maximum likelihood estimator (MLE) for such distributions exists based on $n\geq2$ observations, irrespective of the underlying dimension. Slawski and Hein [Linear Algebra Appl. 473 (2015) 145–179], who first proved…

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…

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…

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…

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…

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…

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…

基于稀疏充分降维的稳健高效因果推断AI 解读

A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in…

时间依赖观测下高维协方差与精度矩阵的估计AI 解读

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that several commonly used methods for independent observations can be applied to the temporally dependent data. In particular, the rates of convergence are obtained for…

高维多响应张量回归的凸正则化AI 解读

In this paper, we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable regularizers assuming that the underlying tensor lies in an unknown low-dimensional subspace. Within our framework, we derive general risk bounds of the resulting estimate under fairly general dependence structure among covariates. Our framework…

高维经济应用中的因子 Lasso 与 k 步 Bootstrap 推断AI 解读

We consider inference about coefficients on a small number of variables of interest in a linear panel data model with additive unobserved individual and time specific effects and a large number of additional time-varying confounding variables. We suppose that, in addition to unrestricted time and individual specific effects, these confounding variables are generated by a small number of common factors and high-dimensional weakly dependent disturbances. We allow that both the…

高维近似稀疏分位数回归模型中的有效选择后推断AI 解读

This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model. We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable approximation to the conditional quantile function. The proposed methods are (explicitly or implicitly) based on orthogonal score functions that protect against moderate model selection…

通信高效的分布式统计推断AI 解读

We present a communication-efficient surrogate likelihood (CSL) framework for solving distributed statistical inference problems. CSL provides a communication-efficient surrogate to the global likelihood that can be used for low-dimensional estimation, high-dimensional regularized estimation, and Bayesian inference. For low-dimensional estimation, CSL provably improves upon naive averaging schemes and facilitates the construction of confidence intervals. For high-dimensional…

析因实验中的因果交互作用：联合分析应用AI 解读

We study causal interaction in factorial experiments, in which several factors, each with multiple levels, are randomized to form a large number of possible treatment combinations. Examples of such experiments include conjoint analysis, which is often used by social scientists to analyze multidimensional preferences in a population. To characterize the structure of causal interaction in factorial experiments, we propose a new causal interaction effect, called the average…

高维贝叶斯向量自回归模型的后验一致性AI 解读

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which provides novel insights into the role of temporal dependence for…

cmenet：条件主效应的双层变量选择方法AI 解读

Simon Maka & C. F. Jeff Wua*a School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GACONTACT C. F. Jeff Wu jeffwu@isye.gatech.edu School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to…

图引导的协方差矩阵带状估计AI 解读

Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on the desired pattern of sparsity. A highly-related, yet complementary, literature studies the specific setting in which the measured variables have a known…

无重复矩阵型数据的均值与协方差联合估计AI 解读

Michael Hornsteina*, Roger Fana, Kerby Sheddena & Shuheng Zhouaba Department of Statistics, University of Michigan, Ann Arbor, MIb Department of Statistics, University of California, Riverside, CACONTACT Michael Hornstein mdhorn@umich.edu Department of Statistics, University of Michigan, Ann Arbor, MI 48109.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available…

平滑变化均值趋势下的方差变点检测及肝脏获取应用AI 解读

Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario, where the variance of data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to the example can yield erroneous change point estimates since the…