每日简报

稀疏线性回归的高效交叉验证AI 解读

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To choose hyperparameters that control the sparsity level and amount of regularization, practitioners commonly use k-fold cross-validation. However, cross-validation substantially increases the computational cost of sparse regression as it…

融合套索下的分段常数风险率估计AI 解读

In applied time-to-event analysis, a flexible and useful approach is to model the hazard rate as a piecewise constant function of time. However, the change points and values of the piecewise constant hazard are usually unknown and need to be estimated. In this paper, we develop a fully data-driven procedure for piecewise constant hazard estimation. We work in a general counting process framework which nests a wide range of popular models in time-to-event analysis including…

非高斯输入下 Volterra 互相关识别的闭式偏度惩罚AI 解读

The monomial parameterization of finite-memory Volterra identification is ill-conditioned under non-Gaussian input, and the Wiener--Hermite expansion removes this ill-conditioning only for Gaussian white-noise input. We construct the distribution-matched Volterra--Wiener--Kunchenko (VWK) basis by oriented Gram--Schmidt orthogonalization of monomials in $L^2(P)$ and use it as an arbitrary-polynomial-chaos coordinate system for finite-memory Volterra identification from data,…

高维随机效应模型信噪比估计的误设定分析AI 解读

Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications, including heritability estimation in bioinformatics. One widely used estimator is the Gaussian random-effects maximum likelihood estimator (MLE), based on the likelihood of the homogeneous Gaussian random-effects model in which both the regression coefficients and the noise variables are assumed to be i.i.d. Gaussian. This paper studies the…

基于再生核扩散模型的测量误差数据去噪AI 解读

The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement devices. Motivated by this challenge, we propose a denoising framework that employs diffusion models to generate denoised data whose distribution closely approximates the unobservable, error-free data, thereby permitting standard data…

高效组套索正则化秩回归与基于模拟的调参AI 解读

High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate the group sparsity regularization. By extending the tuning-free property originally developed for the rank Lasso, we introduce a simulation-based tuning rule and further establish a finite-sample error bound for the resulting…

面向高维数据的快速可扩展逐单元稳健集成方法AI 解读

Variable selection and ensemble methods are central to high-dimensional modelling, enabling the identification of relevant predictors and the construction of stable predictive signals through aggregation across multiple models. However, in practice, high-dimensional data are often affected by cellwise contamination, in which individual cells of the data matrix deviate from the underlying multivariate structure without necessarily making the corresponding observation…

隐私约束下的 Knockoff 推断AI 解读

Model-X knockoff framework offers a model-free variable selection method that ensures finite sample false discovery rate (FDR) control. However, the complexity of generating knockoff variables, coupled with the model-free assumption, presents significant challenges for protecting data privacy in this context. In this paper, we propose a comprehensive framework for knockoff inference within the differential privacy paradigm. Our proposed method guarantees robust privacy…

适者生存的Cox模型：生存数据中的枢轴变量选择AI 解读

We revisit Cox's proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially…

重访确定性计算机实验的惩罚似然估计AI 解读

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it can be plagued by numerical issues in small data settings. The addition of a nugget may help but is not a cure-all. Penalized likelihood methods may improve upon traditional MLE, but their success depends on tuning parameter selection. We…

Metropolis-Hastings 算法中的随机步长AI 解读

The performance of Metropolis-Hastings algorithms is highly sensitive to the choice of step size, and miss-specification can lead to severe loss of efficiency. We study algorithms with randomized step sizes, considering both auxiliary-variable and marginalized constructions. We show that algorithms with a randomized step size inherit weak Poincaré inequalities/spectral gaps from their fixed-step-size counterparts under minimal conditions, and that the marginalized kernel…

高维高斯图模型的 spike-and-slab 贝叶斯计算AI 解读

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the data, and parameter estimates. However, computational demands have limited their application when the number of variables is large, which prompted the use of pseudo-Bayesian approaches. We propose fully Bayesian algorithms that provably…

龟壳聚类：面向判别式聚类的混合方法及其在流式细胞术等数据中的应用AI 解读

Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Overfitting…

预测变量个数发散时基于加权残差过程的回归模型检验AI 解读

The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor dimension diverges: in such regimes, the limiting null and alternative distributions of the ICM statistic degenerate to fixed constants. Moreover, when the number of predictors diverges, the commonly used wild bootstrap no longer…

基于稀疏组Lasso的标记点过程强度估计：法国本土营利性与合作银行网点选址AI 解读

In this paper, we model the locations of five major banks in mainland France, two lucrative and three cooperative institutions based on socio-economic considerations. Locations of banks are collected using web scrapping and constitute a bivariate spatial point process for which we estimate nonparametrically summary functions (intensity, Ripley and cross-Ripley's K functions). This shows that the pattern is highly inhomogenenous and exhibits a clustering effect especially at…

核岭回归的推断AI 解读

We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student preferences in school matching mechanisms--the inferential theory of KRR is not fully known. We construct valid and sharp confidence sets that shrink at nearly the minimax rate, allowing nonstandard regressors. Our bootstrap procedure uses…

高维高斯线性回归中正则化路径变量选择的综合指南AI 解读

This paper provides a comprehensive comparison of complete regularization-path-based variable selection procedures in high-dimensional Gaussian linear regression. Our simulation study stands out from previous ones for several reasons. First, it offers comprehensive guidelines for complete variable selection, from regularization path construction to final variable subset selection. In particular, we compare jointly two convex regularization functions (Lasso and Elastic-Net)…

从不规则且含误差的动物追踪数据推断资源选择与利用分布AI 解读

Habitat selection and space use are fundamental to understanding animal distribution. Traditional methods for quantifying habitat preferences from telemetry data assume regular sampling and negligible measurement error. However, these assumptions are routinely violated in marine systems. Practitioners typically regularize and filter the data before fitting models, but these two-step procedures do not propagate uncertainty from the filtering stage and can yield biased…

连续暴露变量分类化导致模型误设时的无模拟外推AI 解读

Epidemiological studies often categorize continuous exposures for interpretation even when the underlying outcome-exposure association is continuous. The fitted categorical regression is a misspecified model because it replaces the continuous exposure with categories. With measurement error, categorization also misclassifies latent exposure categories, so the observed regression generally targets different means and contrasts. Existing estimating-equation and…

贝叶斯分组回归的变分近似惩罚可信区域AI 解读

We develop a fast and accurate grouped penalized credible region approach for variable selection and prediction in Bayesian high-dimensional regression. Most existing Bayesian methods either are subject to high computational costs due to long Markov Chain Monte Carlo runs or yield ambiguous variable selection results due to non-sparse solution output. The penalized credible region framework yields sparse post-processed estimates that facilitates unambiguous grouped variable…

矩阵变量数据稀疏精度估计的高维收敛速率AI 解读

In several applications, the underlying structure of the data allows for the samples to be organized into a matrix variate form. In such settings, the underlying row and column covariance matrices are fundamental quantities of interest. We focus our attention on two popular estimators that have been proposed in the literature: a penalized sparse estimator called SMGM and a heuristic sample covariance estimator. We establish convergence rates for these estimators in relevant…

高斯图模型下网络复杂度的估计AI 解读

The proportion of edges in a Gaussian graphical model (GGM) characterizes the complexity of its conditional dependence structure. Since edge presence corresponds to a nonzero entry of the precision matrix, estimation of this proportion can be formulated as a large-scale multiple testing problem. We propose an estimator that combines p-values from simultaneous edge-wise tests, conducted under false discovery rate control, with Storey's estimator of the proportion of true null…

平均场朗之万动力学中统计特征学习的几何结构AI 解读

We introduce a geometric formulation of statistical feature learning for supervised regression. Feature learning is defined through a base--fiber decomposition: the base is the feature-side geometry produced by training, and the fiber is the learned feature space where estimation is performed. We prove this property for spherical mean-field Langevin dynamics, viewed as the Wasserstein gradient flow of a negative entropy-regularized empirical risk. In Gaussian multi-index…

边际处理效应函数的一致置信带AI 解读

This paper presents a method for constructing uniform confidence bands for the marginal treatment effect (MTE) function. The shape of the MTE function provides insight into how the unobserved propensity to receive treatment relates to the treatment effect. Our approach visualizes the statistical uncertainty of an estimated function, facilitating inferences about the function's shape. The proposed method is computationally inexpensive and requires only minimal information:…