每日简报

岭回归的无分布置信椭球与PAC界AI 解读

Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically unstable. This issue can be resolved through regularization, typically with ridge regression. Although regularized estimators reduce the variance error, it remains important to quantify their estimation uncertainty. A possible approach for…

高维误设线性模型中岭回归广义交叉验证的一致相合性AI 解读

This study examines generalized cross-validation for the tuning parameter selection for ridge regression in high-dimensional misspecified linear models. The set of candidates for the tuning parameter includes not only positive values but also zero and negative values. We demonstrate that if the second moment of the specification error converges to zero, generalized cross-validation is still a uniformly consistent estimator of the out-of-sample prediction risk. This implies…

稀疏置换线性回归的有限样本推断AI 解读

We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The permutation is a key component of the data-generating process, yet its statistical investigation remains challenging due to its discrete nature. We develop a general statistical inference framework on the permutation and regression coefficients.…

高维线性回归中的参数化平均场经验贝叶斯AI 解读

In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the asymptotic distribution of the variational Empirical Bayes (vEB) estimator, which approximately maximizes a variational lower bound of the intractable marginal likelihood. We characterize a sharp phase transition behavior for the vEB estimator -- namely that it is information theoretically optimal…

测量误差下凹分布函数的推断AI 解读

We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least concave majorant on the positive half-line of the deconvolution estimator of the distribution function. We show its uniform consistency and its square root convergence in law in $\ell_\infty(\mathbb R)$. To assess the validity of the…

基于拟后验的贝叶斯变量选择AI 解读

The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the variables are active and exhibit strong finite-sample performance. However, Bayesian methods require the correct specification of full likelihoods for the data, and there is increasing awareness of the problems that model misspecification…

广义线性模型中的高维高斯与自助法近似AI 解读

Generalized Linear Model (or GLM) extends the ordinary linear regression by linking the mean of the response variable to covariates through appropriate link functions. GLM is widely used in the analysis of datasets arising from diverse fields including medical sciences, clinical trials, population surveys and risk analysis. In this paper, we investigate the Gaussian and Bootstrap approximations of GLM under two separate high dimensional regimes: (I) when the dimension $d$ gro…

稀疏Probit回归的均值场变分贝叶斯方法AI 解读

We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in high-dimensional regimes, we develop a mean-field variational Bayes approximation in which all variational factors admit closed-form updates, and the evidence lower bound is available in closed form. This, in turn, allows the development…

稀疏线性回归中 Lasso 的预测次优性AI 解读

The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the sense that a simple refinement improves upon it both on high-probability events and in mean squared prediction error. Our analysis shows that the relevant stochastic scale is governed by Gaussian maxima on the selected or localized…

黎曼环境流：从受损数据中同时学习流形与生成模型AI 解读

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or linearly corrupted measurements can be observed. Moreover, latent structures, such as manifold geometries, present in the data are important to extract for further downstream scientific analysis. In this work, we introduce Riemannian…

重尾设计下回归的两阶段稳健稀疏梯度方法AI 解读

We study high-dimensional sparse regression under simultaneous heavy-tailed covariates and noise. Heavy-tailed data affect sparse optimization in two different ways: extreme covariates can destabilize the gradient field during global localization, while heavy-tailed noise limits the final statistical accuracy during local refinement. Motivated by this two-phase structure, we propose two-stage RIGHT, a robust sparse first-order method based on coordinate-wise median-of-means…

半敲诈：一种具有有限样本保证的模型无关条件独立性检验方法AI 解读

Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the underlying distribution. However, model-agnostic approaches require a train-test split, which reduces statistical power. We introduce Semi-knockoffs, a CIT method that can accommodate any pre-trained model, avoids this split, and provides…

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…

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…

条件函数图模型中识别差异网络的近邻选择方法AI 解读

Estimating how different brain regions communicate with each other using EEG data is valuable both for medical research and clinical diagnosis. This involves quantifying the statistical dependencies among the activities of different brain areas, captured by the time-varying electric field recorded by scalp sensors. These dependencies can vary within and across individuals also in relationship with external factors such as age, mental state, or disease severity. Motivated by…

多元空间小区域估计中随机效应的全局—局部收缩先验AI 解读

Small area estimation (SAE) plays a central role in survey statistics and epidemiology, providing reliable estimates for domains with limited sample sizes. The multivariate Fay-Herriot model has been extensively used for this purpose, because it enhances estimation accuracy by borrowing strength across multiple correlated variables. In this paper, we develop a Bayesian extension of the multivariate Fay-Herriot model that enables flexible, component-specific shrinkage of the…

基于统计微分方案的抗噪声惩罚算子AI 解读

Classical approaches to penalized smoothing often rely on basis or kernel expansions, which constrain the estimator to a fixed span and may be restrictive for discretely observed data. We instead regularize a single noisy trajectory directly on its observation grid, using difference operators that remain genuine finite-difference approximations to derivatives while being statistically normalized and mutually decorrelated under a reference noise law. We extend this…

大定义域函数型时间序列谱密度的深度学习估计AI 解读

We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators for time series of functions defined on very large grids that arise, for example, in climate compute models and medical scans. Existing estimators use autocovariance kernels represented as large $G \times G$ matrices, where $G$ is the…

稳健小波 NKK 周期图的渐近分布AI 解读

This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time series, we analyze the probabilistic structure of the resulting periodogram under long-range dependence. It is shown that, under suitable regularity conditions, the NKK periodogram converges in distribution to a nonstandard limit…

高维时间序列预测的稀疏 Tucker 分解与图正则化AI 解读

Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a sparse Tucker decomposition method with graph regularization for high-dimensional vector autoregressive time series. By stacking the time-series transition matrices into a third-order tensor, the sparse Tucker decomposition is employed to…

二部网络干扰下的公平政策学习：公平且具成本效益的环境政策AI 解读

Numerous studies have shown the harmful effects of airborne pollutants on human health. Vulnerable groups and communities often bear a disproportionately larger health burden due to exposure to airborne pollutants. Thus, there is a need to design policies that effectively reduce the public health burdens while ensuring cost-effective policy interventions. Designing policies that optimally benefit the population while ensuring equity between groups under cost constraints is a…

结合双重负向控制与图神经网络的双重差分：处理未观测网络混杂AI 解读

Estimating causal effects from observational network data faces dual challenges of network interference and unmeasured confounding. To address this, we propose a general Difference-in-Differences framework that integrates double negative controls (DNC) and graph neural networks (GNNs). Based on the modified parallel trends assumption and DNC, semiparametric identification of direct and indirect causal effects is established. We then propose doubly robust estimators.…

不完全结构模型的分布匹配后验推断AI 解读

This paper introduces a Bayesian inference framework for incomplete structural models, termed distribution-matching posterior inference (DMPI). Extending the minimal econometric interpretation (MEI), DMPI constructs a divergence-based quasi-likelihood using the Jensen-Shannon divergence between theoretical and empirical population-moment distributions, based on a Dirichlet-multinomial structure with additive smoothing. The framework accommodates model misspecification and…

超越 P 值：将金融风险与遗憾指标引入学习型医疗系统的 AI 评价AI 解读

The increasing deployment of artificial intelligence (AI) in clinical settings challenges foundational assumptions underlying traditional frameworks of medical evidence. Classical statistical approaches, centered on randomized controlled trials, frequentist hypothesis testing, and static confidence intervals, were designed for fixed interventions evaluated under stable conditions. In contrast, AI-driven clinical systems learn continuously, adapt their behavior over time, and…