论文检索

通过切片逆回归进行一般指标模型的变量选择AI 解读

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential variables under the general index model, in which the response is dependent of predictors through an unknown function of one or more linear combinations of them. Instead of building a predictive model of the response given combinations of…

大规模 t 检验中错误发现率控制的相变与正则化自助法AI 解读

Applying the Benjamini and Hochberg (B–H) method to multiple Student’s $t$ tests is a popular technique for gene selection in microarray data analysis. Given the nonnormality of the population, the true $p$-values of the hypothesis tests are typically unknown. Hence it is common to use the standard normal distribution $N(0,1)$, Student’s $t$ distribution $t_{n-1}$ or the bootstrap method to estimate the $p$-values. In this paper, we prove that when the population has the…

利用正则化 JIVE 处理大量弱工具变量的工具变量估计AI 解读

We consider instrumental variables regression in models where the number of available instruments may be larger than the sample size and consistent model selection in the first stage may not be possible. Such a situation may arise when there are many weak instruments. With many weak instruments, existing approaches to first-stage regularization can lead to a large bias relative to standard errors. We propose a jackknife instrumental variables estimator (JIVE) with…

贝叶斯桥估计AI 解读

Summary We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: a scale mixture of normal distributions with respect to an α-stable random variable; a mixture of Bartlett–Fejer kernels (or triangle densities) with respect to a two-component mixture of gamma random variables. Both lead to Markov chain Monte Carlo methods for posterior simulation, and these methods turn…

含内生变量的面板数据模型之非参数分析AI 解读

This paper considers the estimation of panel data models by first differences in the presence of endogenous variables and under an instrumental variables condition. This framework leads to the resolution of linear inverse problems solved using a Tikhonov regularization with L2 or Sobolev penalty. Rates of convergence and data driven selection of the regularization parameters are proposed. The practical implementation of our estimators is presented and some Monte Carlo…

基于最小描述长度原则的分段分位数回归模型选择AI 解读

This article proposes new model-fitting techniques for quantiles of an observed data sequence, including methods for data segmentation and variable selection. The main contribution, however, is in providing a means to perform these two tasks simultaneously. This is achieved by matching the data with the best-fitting piecewise quantile regression model, where the fit is determined by a penalization derived from the minimum description length principle. The resulting…

超高维数据的交互项筛选AI 解读

In ultrahigh-dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice is computational feasibility. For a dataset with n observations and p predictors, the augmented design matrix including all linear and order-2 terms is of size n × (p2 + 3p)/2. When p is large, say more than tens of hundreds, the number of interactions is enormous and beyond the capacity of standard machines and software tools for…

稀疏超高维变系数模型中的非参数独立筛选AI 解读

The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection arrives. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in ultra-high dimensional sparse varying-coefficient models. The proposed nonparametric independence screening (NIS) selects…

结合扩展贝叶斯信息准则的序贯 Lasso 超高维特征选择AI 解读

In this article, we propose a method called sequential Lasso (SLasso) for feature selection in sparse high-dimensional linear models. The SLasso selects features by sequentially solving partially penalized least squares problems where the features selected in earlier steps are not penalized. The SLasso uses extended BIC (EBIC) as the stopping rule. The procedure stops when EBIC reaches a minimum. The asymptotic properties of SLasso are considered when the dimension of the…

模型选择后的估计与精度评估AI 解读

Classical statistical theory ignores model selection in assessing estimation accuracy. Here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account. The methodology involves bagging, also known as bootstrap smoothing, to tame the erratic discontinuities of selection-based estimators. A useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators. Two examples,…

基于惩罚样条与狄利克雷过程混合的贝叶斯非参数工具变量回归AI 解读

We propose a Bayesian nonparametric instrumental variable approach under additive separability that allows us to correct for endogeneity bias in regression models where the covariate effects enter with unknown functional form. Bias correction relies on a simultaneous equations specification with flexible modeling of the joint error distribution implemented via a Dirichlet process mixture prior. Both the structural and instrumental variable equation are specified in terms of…

高维阈值回归与收缩效应AI 解读

Summary High dimensional sparse modelling via regularization provides a powerful tool for analysing large-scale data sets and obtaining meaningful interpretable models. The use of non-convex penalty functions shows advantage in selecting important features in high dimensions, but the global optimality of such methods still demands more understanding. We consider sparse regression with a hard thresholding penalty, which we show to give rise to thresholded regression. This…

再生核希尔伯特空间中的结构化函数型加性回归AI 解读

Summary Functional additive models provide a flexible yet simple framework for regressions involving functional predictors. The utilization of a data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting non-linear additive components has been less studied. In this work, we propose a new regularization framework for structure estimation in the context of reproducing kernel…

高维模型中的内生性AI 解读

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized…

折叠凹惩罚估计的强 oracle 最优性AI 解读

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To…

高维非平稳时间序列的广义动态半参数因子模型AI 解读

High‐dimensional non‐stationary time series, which reveal both complex trends and stochastic behaviour, occur in many scientific fields, e.g. macroeconomics, finance, neuroeconomics, etc. To model these, we propose a generalized dynamic semi‐parametric factor model with a two‐step estimation procedure. After choosing smoothed functional principal components as space functions (factor loadings), we extract various temporal trends by employing variable selection techniques for…

自适应非参数工具变量估计：正则化参数的经验选择AI 解读

In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g, is discontinuous and must be regularized to permit consistent estimation. The optimal regularization parameter depends on population characteristics that are unknown in applications. This paper presents a theoretically justified empirical method for choosing the regularization parameter in series estimation. The method adapts to the unknown smoothness of g and other…

通过正则化多分量回归重建源汇关系：北海鳕鱼幼体迁移应用AI 解读

The problem of reconstructing the source-sink dynamics arises in many biological systems. Our research is motivated by marine applications where newborns are passively dispersed by ocean currents from several potential spawning sources to settle in various nursery regions that collectively constitute the sink. The reconstruction of the sparse source-sink linkage pattern, that is, to identify which sources contribute to which regions in the sink, is a challenging task in…

通过惩罚似然选择混合 Copula 模型AI 解读

A fundamental issue of applying a copula method in applications is how to choose an appropriate copula function for a given problem. In this article we address this issue by proposing a new copula selection approach via penalized likelihood plus a shrinkage operator. The proposed method selects an appropriate copula function and estimates the related parameters simultaneously. We establish the asymptotic properties of the proposed penalized likelihood estimator, including…

EMVS：基于 EM 算法的贝叶斯变量选择AI 解读

Despite rapid developments in stochastic search algorithms, the practicality of Bayesian variable selection methods has continued to pose challenges. High-dimensional data are now routinely analyzed, typically with many more covariates than observations. To broaden the applicability of Bayesian variable selection for such high-dimensional linear regression contexts, we propose EMVS, a deterministic alternative to stochastic search based on an EM algorithm which exploits a…

结构突变时间序列的组 LASSOAI 解读

Consider a structural break autoregressive (SBAR) process where j = 1, …, m + 1, {t1, …, tm} are change-points, 1 = t0 < t1 < ⋅⋅⋅ < tm + 1 = n + 1, σ( · ) is a measurable function on , and {ϵt} are white noise with unit variance. In practice, the number of change-points m is usually assumed to be known and small, because a large m would involve a huge amount of computational burden for parameters estimation. By reformulating the problem in a variable selection context, the…

正则化统计估计的通用路径算法AI 解读

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution toward prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints lead to the popular lasso, fused-lasso, and other generalized ℓ1 penalized…

基于测量误差模型选择似然的非参数分类变量选择AI 解读

Using the relationships among ridge regression, LASSO estimation, and measurement error attenuation as motivation, a new measurement-error-model-based approach to variable selection is developed. After describing the approach in the familiar context of linear regression, we apply it to the problem of variable selection in nonparametric classification, resulting in a new kernel-based classifier with LASSO-like shrinkage and variable-selection properties. Finite-sample…

动态基因调控网络建模的稀疏可加常微分方程AI 解读

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and…