每日简报

非可微正则化下低维模式在一般损失函数中的渐近分布AI 解读

This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the underlying structure of the parameter -- which coefficients are zero, which are equal, and how they are clustered. The main technical challenge stems from the discontinuous nature of these patterns (such as the sign function in the case of the…

对抗污染下的稳健回归：Welsch 估计量的理论与算法AI 解读

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex M-estimator, specifically the Welsch estimator, and show that it can eliminate this bias whenever it is statistically identifiable. We focus on high-dimensional linear regression under adversarial contamination, where a fraction of samples may…

通过策略性大数定律进行优化AI 解读

This paper proposes a unified framework for the global optimization of a continuous function in a bounded rectangular domain. Specifically, we show that: (1) under the optimal strategy for a two-armed decision model, the sample mean converges to a global optimizer under the Strategic Law of Large Numbers, and (2) a sign-based strategy built upon the solution of a parabolic PDE is asymptotically optimal. Motivated by this result, we propose a class of {\bf S}trategic {\bf…

分布偏移下的高维分位数回归迁移学习AI 解读

Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional regression setting, existing transfer approaches mainly focus on the parameter shift. In this paper, we focus on the high-dimensional quantile regression with knowledge transfer under three types of distribution shift: parameter shift,…

logistic 对数似然的最优且可计算下界AI 解读

The logit transform is arguably the most widely-employed link function beyond linear settings. This transformation routinely appears in regression models for binary data and provides a central building-block in popular methods for both classification and regression. Its widespread use, combined with the lack of analytical solutions for the optimization of objective functions involving the logit transform, still motivates active research in computational statistics. Among the…

相关线性化的Dyson方程与随机特征回归的检验误差AI 解读

This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression. The theory developed for the correlated Dyson equation includes existence-uniqueness, spectral support bounds, and stability properties. This theory is new for constructing deterministic equivalents for pseudo-resolvents of a class of linearizations with correlated entries.…

高维分组模型选择中的全局-局部先验一致性方法AI 解读

We consider the problem of model selection when grouping structure is inherent within the regressors. Using a Bayesian approach, we model the mean vector by a one-group global-local shrinkage prior belonging to a broad class of such priors that includes the horseshoe prior. In the context of variable selection, this class of priors was studied by Tang et al. (2018). A modified form of the usual class of global-local shrinkage priors with polynomial tail on the group…

高维数据整合中的最优网络引导协变量选择AI 解读

Modern data often arises with multiple modalities. For example, covariates and a network are observed on the same subjects, and both contain useful information. Effectively integrating these modalities is important and challenging, especially when the response is unavailable. We study the fundamental covariate selection problem for high-dimensional data by leveraging network information. We propose the Network-Guided Covariate Selection (NGCS) algorithm. NGCS exploits the…

自适应 Langevin 扩散的动力学平均场分析：复本对称不动点与经验贝叶斯AI 解读

In many applications of statistical estimation via sampling, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already seen. We study an example of such dynamics, given by a Langevin diffusion for posterior sampling in a Bayesian linear regression model with i.i.d. regression design, whose prior continuously adapts to the Langevin trajectory via a maximum marginal-likelihood scheme. Results of dynamical mean-field…

自适应 Langevin 扩散的动力学平均场分析：混沌传播与线性响应收敛AI 解读

Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts to the empirical distribution of the realized process up to the current time. The resulting dynamics take the form of a stochastic interacting particle system having both a McKean-Vlasov type interaction and a pairwise interaction defined…

缺失非随机下基于模型聚类的变量选择统一框架AI 解读

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in…

混合类型结果的高维回归：多元 spike-and-slab LASSOAI 解读

We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from a multivariate linear regression model. Our goal is to estimate simultaneously a sparse matrix ($B$) of latent regression coefficients (i.e., partial covariate effects) and a sparse latent residual precision matrix ($Ω$), which induces…

高维噪声常微分方程中的向量场重构AI 解读

This work investigates the nonparametric estimation of the vector field of a noisy Ordinary Differential Equation (ODE) in high-dimensional ambient spaces, under the assumption that the initial conditions are sampled from a lower-dimensional structure. Specifically, let \( f:\mathbb{R}^{D}\to\mathbb{R}^{D} \) denote the vector field of the autonomous ODE \( y' = f(y) \). We observe noisy trajectories \( \tilde{y}_{X_i}(t_j) = y_{X_i}(t_j) + \varepsilon_{i,j} \), where \( y_{X_i}(t_j) \)…

双重稳健且计算高效的高维变量选择AI 解读

Variable selection can be performed by testing conditional independence (CI) between each predictor and the response, given the other predictors. A doubly robust and powerful option for these CI tests is the projected covariance measure (PCM) test. However, directly deploying PCM for variable selection brings computational challenges: testing a single variable involves a few machine learning fits, so testing $p$ variables requires $O(p)$ fits. Inspired by model-X ideas, we…

分层收缩先验下高斯过程回归的归一化流方法AI 解读

Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and the computational burden, which is particularly acute in fully Bayesian inference. This paper introduces a novel methodology that combines hierarchical global-local shrinkage priors with normalizing flows to address these challenges. The…

Mondrian 随机森林的统计推断AI 解读

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees are constructed via a Mondrian process. We give precise bias and variance characterizations, along with a Berry-Esseen-type central limit theorem, for the Mondrian random forest regression estimator. By combining these results with a…

污染下高维双重稳健因果推断的惩罚经验似然AI 解读

We propose a doubly robust estimator for the average treatment effect in high dimensional low sample size observational studies, where contamination and model misspecification pose serious inferential challenges. The estimator combines bounded influence estimating equations for outcome modeling with covariate balancing propensity scores for treatment assignment, embedded within a penalized empirical likelihood framework using nonconvex regularization. It satisfies the oracle…

孟德尔随机化因果推断方法：估计对象、识别与推断AI 解读

Mendelian randomization (MR) has become an essential tool for causal inference in biomedical and public health research. By using genetic variants as instrumental variables, MR helps address unmeasured confounding and reverse causation, offering a quasi-experimental framework to evaluate causal effects of modifiable exposures on health outcomes. Despite its promise, MR faces substantial methodological challenges, including invalid instruments, weak instrument bias, and…

结合贝叶斯加性回归树的第二类Tobit样本选择模型AI 解读

This paper introduces Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2). BART can produce accurate individual-specific treatment effect estimates. However, in practice estimates are often biased by sample selection. We extend the Type 2 Tobit sample selection model to account for nonlinearities and model uncertainty by including sums of trees in both the selection and outcome equations. A Dirichlet Process Mixture distribution for the error terms allows for…

环境暴露对社会流动的影响：主分层的贝叶斯半参数方法AI 解读

Understanding the causal effects of air pollution exposures on social mobility is attracting increasing attention. At the same time, education is widely recognized as a key driver of social mobility. However, the causal pathways linking fine particulate matter (PM2.5) exposure, educational attainment, and social mobility remain largely unexplored. To address this, we adopt the principal stratification approach, which rigorously defines causal effects when a post-treatment…

弱载荷因子增强回归的预测准确性相等检验AI 解读

We provide the theoretical foundation for the recent tests of equal forecast accuracy and encompassing by Pitarakis (2023) and Pitarakis (2025), when the competing forecast specification is that of a factor-augmented regression model. This should be of interest for practitioners, as there is no theory justifying the use of these simple and powerful tests in such context. In pursuit of this, we employ a novel theory to incorporate the empirically well-documented fact of…

稀疏且稳健的独立成分分析方法AI 解读

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent…

整群随机试验中不完整结果与协变量的处理AI 解读

In cluster-randomized trials (CRTs), missing data can occur in various ways, including missing values in outcomes and baseline covariates at the individual or cluster level, or completely missing information for non-participants. Among the various types of missing data in CRTs, missing outcomes have attracted the most attention. However, no existing methods simultaneously address all aforementioned types of missing data in CRTs. To fill in this gap, we propose a…

连接政策学习中的经验福利最大化与条件平均处理效应估计AI 解读

The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated…