每日简报

共轭域二分法：高维无限方差噪声下M估计的精确风险AI 解读

This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that the asymptotic behavior of a regularized M-estimator is governed by a single geometric property of the loss function: the boundedness of the domain of its Fenchel conjugate. When this conjugate domain is bounded -- as is the case for the…

基于复合的正则化回归：多流分布模型的可识别性、结构化惩罚与统计保证AI 解读

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to flat likelihood regions and unstable estimates. We introduce a structured regularization framework that resolves this issue by assigning flow-specific penalties. The resulting estimator is defined as a penalized maximum likelihood problem…

稳健正则化协方差矩阵估计：适定性与收敛算法AI 解读

In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and structured estimators are given. However, we show that the standard fixed-point algorithm which is usually applied to an M-estimation problem does not necessarily converge for penalized M-estimation problems. Hence, we develop a new but simple…

高维随机划分的纵向共识推断AI 解读

We review recently proposed Bayesian approaches for clustering high-dimensional data. After identifying the main limitations of available approaches, we introduce an alternative framework based on vertical consensus inference (VCI) to mitigate the curse of dimensionality in high-dimensional Bayesian clustering. VCI builds on the idea of consensus Monte Carlo by dividing the data into multiple shards (smaller subsets of variables), performing posterior inference on each…

面向MNAR数据的可识别深度潜变量模型AI 解读

Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is independent of the missing values themselves. This assumption is frequently violated in real-world scenarios, prompted by recent advances in imputation methods using deep learning to address this challenge. However, these methods neglect the…

识别应得决策规则以评估与实现公平AI 解读

We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for characterising and addressing fairness issues by introducing the notion of desert decision, a latent variable representing the decision an individual rightfully deserves based on their actions, efforts, or abilities. This formulation shifts…

高斯噪声下投影算子的估计AI 解读

This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying subspace. The provided upper bounds depend on the noise and on intrinsic properties of the estimated subspace. Several scenarios are considered according to the distribution of the estimator of the matrix spanning the subspace. The…

DROP：图模型多任务学习中的分布鲁棒优化AI 解读

Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and heavy-tailed noise. In this paper, we propose DROP (Distributionally Robust Optimization), a robust estimation method formulated within a multi-task nodewise regression framework. The proposed estimator enforces structural sparsity while…

基于结构化得分匹配的无似然推断AI 解读

In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We develop a likelihood-free inference framework that combines score matching with gradient-based optimization and bootstrap procedures to facilitate parameter estimation together with uncertainty quantification. The proposed methodology…

超越错误发现率：面向分组变量选择的逐步分组 SLOPE 方法AI 解读

High-dimensional feature selection is routinely required to balance statistical power with strict control of multiple-error metrics such as the k-Family-Wise Error Rate (k-FWER) and the False Discovery Proportion (FDP), yet some existing frameworks are confined to the narrower goal of controlling the expected False Discovery Rate (FDR) and can not exploit the group-structure of the covariates, such as Sorted L-One Penalized Estimation (SLOPE). We introduce the Group Stepdown…

利用稀疏性提升分层贝叶斯模型的No-U-Turn采样效率AI 解读

Analysts routinely use Bayesian hierarchical models to understand natural processes. The no-U-turn sampler (NUTS) is the most widely used algorithm to sample high-dimensional, continuously differentiable models. But NUTS is slowed by high correlations, especially in high dimensions, limiting the complexity of applied analyses. Here we introduce Sparse NUTS (SNUTS), which preconditions (decorrelates and descales) posteriors using a sparse precision matrix ($Q$). We use…

增广 van Trees 不等式AI 解读

We introduce an augmented form of the van Trees inequality, that yields uniformly tighter lower bounds on the minimax squared Bayes risk of estimators compared with the classical van Trees inequality. Our augmented inequality also accommodates prior distributions whose densities need not vanish at the boundaries of their supports. We demonstrate how this refinement can be utilised for elementary proofs of a number of minimax lower bounds for nonparametric estimands, that…

离散观测下高维Lévy驱动OU过程的稀疏估计AI 解读

We study high-dimensional drift estimation for Lévy-driven Ornstein--Uhlenbeck processes based on discrete observations. Assuming sparsity of the drift matrix, we analyze Lasso and Slope estimators constructed from approximate likelihoods and derive sharp nonasymptotic oracle inequalities. Our bounds disentangle the contributions of discretization error and stochastic fluctuations, and establish minimax optimal convergence rates under suitable choices of tuning parameters in…

面向含噪输入数据的树基预测模型AI 解读

Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small samples from a much larger, generally unobserved system and reflect both sampling error and technical variation. In high-noise settings like these, it becomes difficult to make accurate predictions and to summarize uncertainty. Methods have…

隐私线性回归中适应噪声尾部的方法AI 解读

While the traditional goal of statistics is to infer population parameters, modern practice increasingly demands protection of individual privacy. One way to address this need is to adapt classical statistical procedures into privacy-preserving algorithms. In this paper, we develop differentially private tail-robust methods for linear regression. The trade-off among bias, privacy, and robustness is controlled by a tunable robustification parameter in the Huber loss. We…

函数型回归中变量选择的变分推断AI 解读

In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction accuracy. In this work, we develop a variational inference approach for estimation and variable selection in scalar-on-function regression, involving only functional covariates, and in partially functional regression models that also…

基于分区的函数型岭回归：高维数据方法AI 解读

This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability in high-dimensional functional linear models. The coefficient function vector \( \boldsymbolβ(s) \) is decomposed into two components, \( \boldsymbolβ_1(s) \) and \( \boldsymbolβ_2(s) \), representing dominant and weaker functional effects. This partition enables differential ridge penalization across functional blocks, so that important…

面向连续与二元混合响应的稳健联合建模AI 解读

In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate analyses. But outliers pose a new challenge to the existing likelihood-based modeling approaches. In this paper, we propose a new robust joint modeling framework for data with both continuous and binary responses. It is based on the…

批量贝叶斯最优实验设计的 Wasserstein 梯度流AI 解读

Bayesian optimal experimental design (BOED) provides a powerful, decision-theoretic framework for selecting experiments so as to maximise the expected utility of the data to be collected. In practice, however, its applicability can be limited by the difficulty of optimising the chosen utility. The expected information gain (EIG), for example, is often high-dimensional and strongly non-convex. This challenge is particularly acute in the batch setting, where multiple…

参数与半参数方法下的变量选择与响应误分类AI 解读

While variable selection has received extensive attention in the literature, its exploration in the presence of response measurement error remains underexplored. In this paper, we investigate this important problem within the context of binary classification with error-prone responses. We present valid variable selection procedures to address the complexities of response errors. Leveraging validation data, we introduce both parametric and semiparametric methodologies to…

高维回归系数的秩基 Maxsum 检验AI 解读

We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives, practical applications rarely reveal the sparsity level, and many existing procedures rely on light-tail assumptions. Motivated by the Wilcoxon-score sum test of Feng et al. (2013) and the two Wilcoxon-score maximum tests of Xu and Zhou (2021),…

Wasserstein 分布稳健分位数回归AI 解读

We study distributionally robust quantile regression using type-$p$ Wasserstein ambiguity sets. We derive a closed-form expression for the worst-case quantile regression loss under general $p$-Wasserstein uncertainty. We further give a uniqueness result showing that for $p>1$, the check loss yields the only class of convex loss functions for which such an additive Wasserstein regularization holds. Our analysis also uncovers qualitative differences between the regimes $p=1$ an…

最优决策树的统计最优性AI 解读

While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we develop a comprehensive statistical theory for ERM trees under random design in both high-dimensional regression and classification. We first establish sharp oracle inequalities that bound the excess risk of the ERM estimator relative to the…

高维缺失数据估计：统计与计算极限AI 解读

We consider computationally-efficient estimation of population parameters when observations are subject to missing data. In particular, we consider estimation under the realizable contamination model of missing data in which an $ε$ fraction of the observations are subject to an arbitrary (and unknown) missing not at random (MNAR) mechanism. When the true data is Gaussian, we provide evidence towards statistical-computational gaps in several problems. For mean estimation in $\ell_2$…