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采用收缩与扩散先验的贝叶斯变量选择AI 解读

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in…

协变量维数增长时相关数据的广义可加部分线性模型估计与选择AI 解读

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood…

非参数回归中基于平方根 Lasso 的枢轴估计AI 解读

We propose a self-tuning $\sqrt{\mathrm {Lasso}} $ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in…

对《lasso 的显著性检验》讨论的回复AI 解读

We would like to thank the Editors and referees for their considerable efforts that improved our paper, and all of the discussants for their feedback, and their thoughtful and stimulating comments.Linear models are central in applied statistics, and inference for adaptive linear modeling is an important active area of research.Our paper is clearly not the last word on the subject.Several of the discussants introduce novel proposals for this problem; in fact, many of the…

讨论：《Lasso 的显著性检验》AI 解读

The paper by Lockhart, Taylor, Tibshirani and Tibshirani (LTTT) is an important advancement in our understanding of inference for high-dimensional regression.The paper is a tour de force, bringing together an impressive array of results, culminating in a set of very satisfying convergence results.The fact that the test statistic automatically balances the effect of shrinkage and the effect of adaptive variable selection is remarkable.The authors make very strong…

lasso的显著性检验AI 解读

In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the covariance test statistic, and show that when the true model is linear, this statistic has an $\operatorname{Exp}(1)$ asymptotic distribution under the null hypothesis (the null being that all…

基于 lasso 惩罚 D-trace 损失的稀疏精度矩阵估计AI 解读

We introduce a constrained empirical loss minimization framework for estimating high-dimensional sparse precision matrices and propose a new loss function, called the D-trace loss, for that purpose. A novel sparse precision matrix estimator is defined as the minimizer of the lasso penalized D-trace loss under a positive-definiteness constraint. Under a new irrepresentability condition, the lasso penalized D-trace estimator is shown to have the sparse recovery property.…

正则化矩阵回归AI 解读

Summary Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry and electroencephalography, matrix-type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are…

用于多类别逆协方差估计的联合图形套索AI 解读

Summary We consider the problem of estimating multiple related Gaussian graphical models from a high dimensional data set with observations belonging to distinct classes. We propose the joint graphical lasso, which borrows strength across the classes to estimate multiple graphical models that share certain characteristics, such as the locations or weights of non-zero edges. Our approach is based on maximizing a penalized log-likelihood. We employ generalized fused lasso or…

稀疏情形下用于变量选择的信息准则AI 解读

The optimization of an information criterion in a variable selection procedure leads to an additional bias, which can be substantial for sparse, high-dimensional data. One can compensate for the bias by applying shrinkage while estimating within the selected models. This paper presents modified information criteria for use in variable selection and estimation without shrinkage. The analysis motivating the modified criteria follows two routes. The first, which we explore for…

联合 L1 与凹惩罚正则化的渐近性质AI 解读

Two important goals of high-dimensional modelling are prediction and variable selection. In this article, we consider regularization with combined L1 and concave penalties, and study the sampling properties of the global optimum of the suggested method in ultrahigh-dimensional settings. The L1 penalty provides the minimum regularization needed for removing noise variables in order to achieve oracle prediction risk, while a concave penalty imposes additional regularization to…

通过趋势滤波进行自适应分段多项式估计AI 解读

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339–360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute $k$th order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of $k$th degree spline functions, with adaptively chosen knot points (we say…

自适应稳健变量选择AI 解读

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted $L_1$-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the $L_1$-penalty. In the ultra-high dimensional setting, where the dimensionality can grow…

超高维协变量变系数模型的特征选择AI 解读

This paper is concerned with feature screening and variable selection for varying coefficient models with ultrahigh dimensional covariates. We propose a new feature screening procedure for these models based on conditional correlation coefficient. We systematically study the theoretical properties of the proposed procedure, and establish their sure screening property and the ranking consistency. To enhance the finite sample performance of the proposed procedure, we further…

半参数线性模型中的贝叶斯变量选择AI 解读

There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures of g-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g-prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation…

倾向得分估计的不确定性：贝叶斯变量选择与模型平均因果效应AI 解读

Causal inference with observational data frequently relies on the notion of the propensity score (PS) to adjust treatment comparisons for observed confounding factors. As decisions in the era of "big data" are increasingly reliant on large and complex collections of digital data, researchers are frequently confronted with decisions regarding which of a high-dimensional covariate set to include in the PS model in order to satisfy the assumptions necessary for estimating…

DAE-seq 数据分析：变量选择与观测依赖建模AI 解读

In DAE (DNA After Enrichment)-seq experiments, genomic regions related with certain biological processes are enriched/isolated by an assay and are then sequenced on a high-throughput sequencing platform to determine their genomic positions. Statistical analysis of DAE-seq data aims to detect genomic regions with significant aggregations of isolated DNA fragments ("enriched regions") versus all the other regions ("background"). However, many confounding factors may influence…

广义最小二乘矩阵分解AI 解读

Variables in many big-data settings are structured, arising, for example, from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performance. We propose a generalization of principal components analysis (PCA) that is appropriate for massive datasets with structured variables or known two-way dependencies. By…

高维回归的模型平均方法AI 解读

This article considers high-dimensional regression problems in which the number of predictors p exceeds the sample size n. We develop a model-averaging procedure for high-dimensional regression problems. Unlike most variable selection studies featuring the identification of true predictors, our focus here is on the prediction accuracy for the true conditional mean of y given the p predictors. Our method consists of two steps. The first step is to construct a class of…

分位数回归模型的贝叶斯信息准则选择AI 解读

Bayesian information criterion (BIC) is known to identify the true model consistently as long as the predictor dimension is finite. Recently, its moderate modifications have been shown to be consistent in model selection even when the number of variables diverges. Those works have been done mostly in mean regression, but rarely in quantile regression. The best-known results about BIC for quantile regression are for linear models with a fixed number of variables. In this…

广义矩方法的自适应弹性网AI 解读

Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation…

利用非参数方法高效估计有限总体非线性参数AI 解读

Summary Currently, high precision estimation of non-linear parameters such as Gini indices, low income proportions or other measures of inequality is particularly crucial. We propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a non-parametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any…

条件变换模型AI 解读

Summary The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and…

非参数工具变量回归中含噪非线性算子方程的迭代估计AI 解读

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach…