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可逆序列记忆长度的贝叶斯正则化AI 解读

Summary Variable order Markov chains have been used to model discrete sequential data in a variety of fields. A host of methods exist to estimate the history-dependent lengths of memory which characterize these models and to predict new sequences. In several applications, the data-generating mechanism is known to be reversible, but combining this information with the procedures mentioned is far from trivial. We introduce a Bayesian analysis for reversible dynamics, which…

稀疏包络模型：多元线性回归的高效估计与响应变量选择AI 解读

The envelope model allows efficient estimation in multivariate linear regression. In this paper, we propose the sparse envelope model, which is motivated by applications where some response variables are invariant with respect to changes of the predictors and have zero regression coefficients. The envelope estimator is consistent but not sparse, and in many situations it is important to identify the response variables for which the regression coefficients are zero. The…

含分组预测变量的广义线性模型：微分几何方法AI 解读

We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important properties that distinguish it from the group lasso. First, its solution curve is based on the invariance properties of a generalized linear model. Second, it adds groups of…

失效时间结局病例队列研究中的变量选择AI 解读

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of a variable selection procedure using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality…

正则化对谱聚类的影响AI 解读

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et al. [Ann. Statist. 41 (2013) 2097–2122]. Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario…

利用过完备字典求解线性不适定问题AI 解读

In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions,…

海量异质数据的部分线性框架AI 解读

We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (non-asymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. This oracular result holds when the number of sub-populations…

用于基因网络推断的两阶段自适应 Lasso 有向无环图估计AI 解读

Graphical models are a popular approach to find dependence and conditional independence relationships between gene expressions. Directed acyclic graphs (DAGs) are a special class of directed graphical models, where all the edges are directed edges and contain no directed cycles. The DAGs are well known models for discovering causal relationships between genes in gene regulatory networks. However, estimating DAGs without assuming known ordering is challenging due to high…

稀疏超高维变系数模型的前向变量选择AI 解读

Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow for flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it is challenging to select the relevant variables when the dimensionality is very large. Recently, several works are focused on this important problem based on sparsity assumptions; they are subject to some limitations, however. We…

面板结果的贝叶斯处理效应与变量选择：产假对收入的影响AI 解读

We propose two alternative Bayesian treatment effect modeling and inferential frameworks for panel outcomes to estimate dynamic earnings effects of a long maternity leave on mothers’ subsequent earnings. Modeling of the endogeneity of the treatment and the panel structure of the earnings are based on the modeling tradition of the Roy switching regression model and the shared factor approach, respectively. We implement stochastic variable selection to test, for example, for…

用于变量筛选的高维普通最小二乘投影AI 解读

Summary Variable selection is a challenging issue in statistical applications when the number of predictors p far exceeds the number of observations n. In this ultrahigh dimensional setting, the sure independence screening procedure was introduced to reduce the dimensionality significantly by preserving the true model with overwhelming probability, before a refined second-stage analysis. However, the aforementioned sure screening property strongly relies on the assumption…

基于剖面优化的单指标分位数回归推断AI 解读

Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score…

SLOPE 对未知稀疏度的自适应性与渐近极小极大性AI 解读

We consider high-dimensional sparse regression problems in which we observe $\mathbf{y}=\mathbf{X}\boldsymbol{\beta} +\mathbf{z}$, where $\mathbf{X}$ is an $n\times p$ design matrix and $\mathbf{z}$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\sigma^{2}$. Our focus is on the recently introduced SLOPE estimator [Ann. Appl. Stat. 9 (2015) 1103–1140], which regularizes the least-squares estimates with the rank-dependent penalty $\sum_{1\le i\le p}\lambda_{i}|\widehat{\beta} |_{(i)}$…

特征值非参数正则化的精度矩阵与协方差矩阵估计AI 解读

We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger…

精确的事后选择推断及其在 lasso 中的应用AI 解读

We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.

利用采购经理指数预测产出增长的多国方法AI 解读

This paper derives new theoretical results for forecasting with Global VAR (GVAR) models. It is shown that the presence of strong unobserved common factors can lead to an undetermined GVAR model. To solve this problem, we propose augmenting the GVAR with additional proxy equations for the strong factors and establish conditions under which forecasts from the augmented GVAR model (AugGVAR) uniformly converge in probability (as the panel dimensions N,T→j∞) to the infeasible…

TENET：尾部事件驱动的网络风险AI 解读

CoVaR is a measure for systemic risk of the networked financial system conditional on institutions being under distress. The analysis of systemic risk is the focus of recent econometric analyses and uses tail event and network based techniques. Here, in this paper we bring tail event and network dynamics together into one context. In order to pursue such joint efforts, we propose a semiparametric measure to estimate systemic interconnectedness across financial institutions…

凸性约束下非参数工具变量回归的不适定性AI 解读

This note shows that adding monotonicity or convexity constraints on the regression function does not restore well‐posedness in nonparametric instrumental variable regression. The minimum distance problem without regularization is still locally ill‐posed.

序贯回归程序的精确选择后推断AI 解读

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso…

迹追踪：无模型变量选择的一般框架AI 解读

We propose trace pursuit for model-free variable selection under the sufficient dimension-reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection consistency with fixed p. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality. The screening consistency property of forward trace pursuit based on sliced inverse…

稳健正交补主成分分析AI 解读

Recently, the robustification of principal component analysis (PCA) has attracted lots of attention from statisticians, engineers, and computer scientists. In this work, we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is…

变量数远超样本量时典型判别向量的同步稀疏估计AI 解读

This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when p ≫ N. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, G − 1 canonical vectors can be considered if the number of groups is G. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is…

纳入预测变量图结构的稀疏回归AI 解读

With the abundance of high dimensional data in various disciplines, sparse regularized techniques are very popular these days. In this paper, we make use of the structure information among predictors to improve sparse regression models. Typically, such structure information can be modeled by the connectivity of an undirected graph using all predictors as nodes of the graph. Most existing methods use this undirected graph edge-by-edge to encourage the regression coefficients…

用于高维分类的贝叶斯条件张量分解AI 解读

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors. In settings such as genomics, there can be complex interactions among the predictors. By using a carefully-structured Tucker factorization, we define a model that can characterize any conditional probability, while facilitating variable…