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RaSE：基于随机子空间集成的变量筛选框架AI 解读

Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to the response. As a result, variables that are marginally independent but jointly dependent with the response could be missed. In this work, we propose a new framework for variable screening, random subspace ensemble (RaSE), which works by…

大规模结构化潜在属性分析的联合最大似然方法AI 解读

Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent attributes explain the dependence of observed variables in a highly structured fashion. Usually, the maximum marginal likelihood estimation approach is adopted for SLAMs, treating the latent attributes as random effects. The increasing scope of…

基于最近邻方法的高维正态性检验AI 解读

Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the Type I error when the dimension is larger than the number of observations. In this work, we propose a novel nonparametric test that uses the nearest neighbor information. The proposed method guarantees the asymptotic Type I error control under the…

通过推断潜在位置估计同质性社会网络中的因果同伴影响AI 解读

Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, that is, with a node’s network partners being informative about the node’s attributes and therefore its behavior. If the network grows according to either a latent community (stochastic block) model, or a continuous latent space model, then latent homophilous attributes can be consistently estimated from the global…

通过对称化数据聚合控制一般依赖下的错误发现率AI 解读

We develop a new class of distribution-free multiple testing rules for false discovery rate (FDR) control under general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening, and information pooling. The proposed SDA filter first constructs a sequence of ranking statistics that fulfill global symmetry properties, and then chooses a data-driven threshold along…

用于正则化非线性回归的随机树集成AI 解读

This article develops a novel stochastic tree ensemble method for nonlinear regression, referred to as accelerated Bayesian additive regression trees, or XBART. By combining regularization and stochastic search strategies from Bayesian modeling with computationally efficient techniques from recursive partitioning algorithms, XBART attains state-of-the-art performance at prediction and function estimation. Simulation studies demonstrate that XBART provides accurate point-wise…

高维混杂下加性风险模型的治疗效应估计AI 解读

Estimating treatment effects for survival outcomes in the high-dimensional setting is critical for many biomedical applications and any application with censored observations. This article establishes an “orthogonal” score for learning treatment effects, using observational data with a potentially large number of confounders. The estimator allows for root-n, asymptotically valid confidence intervals, despite the bias induced by the regularization. Moreover, we develop a…

通过匹配恢复潜在变量AI 解读

We propose an optimal-transport-based matching method to nonparametrically estimate linear models with independent latent variables. The method consists in generating pseudo-observations from the latent variables, so that the Euclidean distance between the model’s predictions and their matched counterparts in the data is minimized. We show that our nonparametric estimator is consistent, and we document that it performs well in simulated data. We apply this method to study…

适用于空间依赖数据的随机森林AI 解读

Spatial linear mixed-models, consisting of a linear covariate effect and a Gaussian process (GP) distributed spatial random effect, are widely used for analyses of geospatial data. We consider the setting where the covariate effect is nonlinear. Random forests (RF) are popular for estimating nonlinear functions but applications of RF for spatial data have often ignored the spatial correlation. We show that this impacts the performance of RF adversely. We propose RF-GLS, a…

不完美随机实验中因果效应的非参数界AI 解读

Nonignorable missingness and noncompliance can occur even in well-designed randomized experiments, making the intervention effect that the experiment was designed to estimate nonidentifiable. Nonparametric causal bounds provide a way to narrow the range of possible values for a nonidentifiable causal effect with minimal assumptions. We derive novel bounds for the causal risk difference for a binary outcome and intervention in randomized experiments with nonignorable…

线性样条模型中的结点估计AI 解读

The linear spline model is able to accommodate nonlinear effects while allowing for an easy interpretation. It has significant applications in studying threshold effects and change-points. However, its application in practice has been limited by the lack of both rigorously studied and computationally convenient method for estimating knots. A key difficulty in estimating knots lies in the nondifferentiability. In this article, we study influence functions of regular and…

个体化群组学习AI 解读

Many massive data sets are assembled through collections of information of a large number of individuals in a population. The analysis of such data, especially in the aspect of individualized inferences and solutions, has the potential to create significant value for practical applications. Traditionally, inference for an individual in the dataset is either solely relying on the information of the individual or from summarizing the information about the whole population.…

大规模向量自回归移动平均模型的稀疏识别与估计AI 解读

The Vector AutoRegressive Moving Average (VARMA) model is fundamental to the theory of multivariate time series; however, identifiability issues have led practitioners to abandon it in favor of the simpler but more restrictive Vector AutoRegressive (VAR) model. We narrow this gap with a new optimization-based approach to VARMA identification built upon the principle of parsimony. Among all equivalent data-generating models, we use convex optimization to seek the…

经验最佳预测量的同时推断及小区域贫困研究AI 解读

Today, generalized linear mixed models (GLMM) are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under…

随机点积图潜在位置的高效一步估计AI 解读

We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods, the proposed one-step procedure takes advantage of both the low-rank structure of the expected adjacency matrix and the Bernoulli likelihood information of the sampling model simultaneously. We show that for each vertex, the corresponding row of the one-step estimator (OSE) converges to a multivariate normal distribution…

潜在高斯计数时间序列AI 解读

This article develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any prespecified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial structures. Gaussian pseudo-likelihood and implied Yule–Walker…

适应模型的回归检验混合方法AI 解读

In model checking for regressions, nonparametric estimation-based tests usually have tractable limiting null distributions and are sensitive to oscillating alternative models, but suffer from the curse of dimensionality. In contrast, empirical process-based tests can, at the fastest possible rate, detect local alternatives distinct from the null model, yet are less sensitive to oscillating alternatives and rely on Monte Carlo approximation for critical value determination,…

相关张量分解及其在空间影像数据中的应用AI 解读

Multi-dimensional tensor data have gained increasing attention in the recent years, especially in biomedical imaging analyses. However, the most existing tensor models are only based on the mean information of imaging pixels. Motivated by multimodal optical imaging data in a breast cancer study, we develop a new tensor learning approach to use pixel-wise correlation information, which is represented through the higher order correlation tensor. We proposed a novel…

动态交互半参数函数对标量回归模型AI 解读

Motivated by recent work studying massive functional data, such as the COVID-19 data, we propose a new dynamic interaction semiparametric function-on-scalar (DISeF) model. The proposed model is useful to explore the dynamic interaction among a set of covariates and their effects on the functional response. The proposed model includes many important models investigated recently as special cases. By tensor product B-spline approximating the unknown bivariate coefficient…

凸性约束单指标模型中的半参数效率AI 解读

We consider estimation and inference in a single-index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least-square estimator (CLSE) for both the parametric and the nonparametric components given independent and identically distributed observations. We prove the consistency and find the rates of convergence of the CLSE when the errors are assumed to have only q≥2 moments and are allowed to depend on the covariates. When…

基于谱主体特征值匹配的协方差尖峰特征值数量估计AI 解读

The spiked covariance model has gained increasing popularity in high-dimensional data analysis. A fundamental problem is determination of the number of spiked eigenvalues, K. For estimation of K, most attention has focused on the use of top eigenvalues of sample covariance matrix, and there is little investigation into proper ways of using bulk eigenvalues to estimate K. We propose a principled approach to incorporating bulk eigenvalues in the estimation of K. Our method…

通过投影与收缩构造高维回归的诚实置信集AI 解读

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level often happens after estimating the degree of smoothness. Similarly, for high-dimensional regression, oracle inequalities for sparse estimators could be utilized to construct sharp confidence sets. Yet the degree of sparsity itself is…

广义 Oaxaca–Blinder 估计量AI 解读

After performing a randomized experiment, researchers often use ordinary least-square (OLS) regression to adjust for baseline covariates when estimating the average treatment effect. It is widely known that the resulting confidence interval is valid even if the linear model is misspecified. In this article, we generalize that conclusion to covariate adjustment with nonlinear models. We introduce an intuitive way to use any “simple” nonlinear model to construct a…

随机梯度下降中的在线协方差矩阵估计AI 解读

The stochastic gradient descent (SGD) algorithm is widely used for parameter estimation, especially for huge datasets and online learning. While this recursive algorithm is popular for computation and memory efficiency, quantifying variability and randomness of the solutions has been rarely studied. This article aims at conducting statistical inference of SGD-based estimates in an online setting. In particular, we propose a fully online estimator for the covariance matrix of…