论文检索

通过逐坐标高斯化检验高维独立性与条件独立性AI 解读

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each component variable to the standard normal via its marginal empirical distribution, and we then test for independence and conditional independence of the transformed random vectors using appropriate L∞-type test statistics. While we are testing…

流形时间序列的平稳性AI 解读

In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is “stationarity”, which reflects the underlying dynamic behavior and is crucial across various fields like cell biology, neuroscience and empirical finance. Yet, there has been an absence of a formal definition of stationarity that is tailored to manifold time series. This work bridges this gap by proposing the first definitions of…

分担负担：公平性调整的分类方法AI 解读

We investigate the fairness issue in classification, where automated decisions are made for individuals from different protected groups. In high-consequence scenarios, decision errors can disproportionately affect certain protected groups, leading to unfair outcomes. To address this issue, we propose a fairness-adjusted selective inference (FASI) framework and develop data-driven algorithms that achieve statistical parity by controlling the false selection rate (FSR) among…

高维线性回归中的残差重要性加权迁移学习AI 解读

Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for high-dimensional linear models built on penalized likelihood. Compared to existing methods such as Trans-Lasso that selects sources in an (approximately) all-in-or-all-out manner, RIW-TL includes samples via importance weighting and thus…

异质轨迹的函数型奇异值分解：健康领域案例AI 解读

Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across subjects such as patients, sites, and subpopulations, yet many traditional methods are not designed to accommodate such heterogeneity in data analysis. To address this, we propose a unified framework, termed Functional Singular Value…

内蕴黎曼函数型充分降维及其扩展AI 解读

This article focuses on linear sufficient dimension reduction with Riemannian random processes as predictors and complex random objects in a metric space as responses. We propose two novel methods—Intrinsic Riemannian Functional Weighted Inverse Regression Ensemble (iRF-WIRE) and Intrinsic Riemannian Functional Weighted Directional Regression (iRF-WDR)—to recover the central subspace. These methods can be readily extended to Wasserstein functional predictors. We establish…

一致有界邻域干扰下的因果推断AI 解读

Abstract Randomized experiments remain the gold standard for estimating treatment effects; however, network interference compromises the validity of traditional estimators by violating the stable unit treatment value assumption and introducing bias. Although cluster-randomized designs help mitigate some bias, they struggle to accommodate complex network structures and cannot disentangle direct from indirect effects. To address these challenges, we develop a design-based…

收入不平等与就业创造AI 解读

Abstract We propose a novel channel through which rising income inequality affects job creation and macroeconomic outcomes. High-income households save relatively more in stocks and bonds but less in bank deposits. A rising top income share thereby increases the relative financing cost for bank-dependent firms, which in turn create fewer jobs compared to other firms. Exploiting variation in top income shares across US states and an instrumental variable strategy, we provide…

KL-BSS：重新审视结构方程模型邻域选择的最优性AI 解读

Abstract We introduce a new method for neighbourhood selection in linear structural equation models that improves over classical methods such as best subset selection (BSS) and the Lasso. Our method, called KL-BSS, takes advantage of the existence of underlying structure in SEM—even when this structure is unknown—and is easily implemented using existing solvers. Under weaker eigenvalue conditions compared to BSS and the Lasso, KL-BSS can provably recover the support of…

极值图模型中的参数与非参数对称性AI 解读

Abstract Coloured graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of colouring for extremal graphical models on generalized multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of the generalized multivariate Pareto distributions, coloured extremal tree models can be…

利用随机化网估计量分位数构造准蒙特卡洛置信区间AI 解读

Recent advances in quasi-Monte Carlo integration have shown that for linearly scrambled digital net estimators, the convergence rate can be dramatically improved by taking the median rather than the mean of multiple independent replicates. In this work, we demonstrate that the quantiles of such estimators can be used to construct confidence intervals with asymptotically valid coverage for high-dimensional integrals. By analyzing the error distribution for a class of…

置换混合分布的近似独立性AI 解读

We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call permutation mixtures) and their i.i.d. counterparts. Our results are based on a novel method for controlling χ2 divergences between exchangeable mixtures, which is tighter than the existing methods of moments or cumulants. At a technical level, a key innovation in our proofs is a new Maclaurin-type inequality for elementary symmetric polynomials of variables…

张量补全中的统计推断：最优不确定性量化与统计计算差距AI 解读

This paper presents a simple yet efficient method for statistical inference of tensor linear forms using incomplete and noisy observations. Under the Tucker low-rank tensor model and the missing-at-random assumption, we utilize an appropriate initial estimate along with a debiasing technique followed by a one-step power iteration to construct an asymptotically normal test statistic. This method is suitable for various statistical inference tasks, including constructing…

经验风险最小化中的梯度下降推断AI 解读

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader potential for statistical inference applications. This paper provides a precise, nonasymptotic joint distributional characterization of gradient descent iterates and their debiased statistics in a broad class of empirical risk minimization…

迈向个体层面数据融合的统一半参数理论AI 解读

We consider inference about a finite-dimensional parameter integrating samples from independent sources. A recently developed theory considers scenarios where sources align with subsets of the conditional distributions of a single factorization of the joint target distribution. While this theory applies in many settings, it falls short in important data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological…

非零中位数 GARCH 型噪声下重尾 AR 模型的两步估计AI 解读

This paper develops a novel two-step estimating procedure for heavy-tailed AR models with nonzero median GARCH-type noises, allowing for time-varying volatility. We first establish the self-weighted quantile regression estimator (SQE) across all quantile levels τ∈(0,1) for the AR parameters θ0. We show that the SQE, less a bias, converges weakly to a Gaussian process at a rate of n−1/2. The bias is zero if and only if τ equals τ0, the probability that the noise is less than…

线性模型迭代算法的不确定性量化及其早停应用AI 解读

This paper investigates the iterates bˆ1,…,bˆT obtained from iterative algorithms in high-dimensional linear regression problems, in the regime where the feature dimension p is comparable with the sample size n, that is, p≍n. The analysis and proposed estimators are applicable to Gradient Descent (GD), proximal GD and their accelerated variants such as Fast Iterative Soft-Thresholding (FISTA). The paper proposes novel estimators for the generalization error of the iterate…

多项式时间内达到极小极大最优的排序恢复AI 解读

We consider the seriation problem, whose goal is to recover a hidden ordering from a noisy observation of a permuted Robinson matrix. We establish sharp minimax rates under average-Lipschitz conditions that strictly extend the bi-Lipschitz framework of Giraud, Issartel and Verzelen (Electron. J. Stat. (2023) 17 1587–1662). We further design a polynomial-time algorithm that attains these optimal rates, thereby resolving two open questions raised in Giraud, Issartel and…

利用广义距离相关检验独立性AI 解读

We study the fundamental statistical inference concerning the testing of independence between two random vectors. Existing asymptotic theories for test statistics based on distance covariance can only apply to either low-dimensional or high-dimensional settings and require stringent distributional assumptions. In this work we develop a new unified distributional theory of the sample generalized distance covariance that works for random vectors of arbitrary dimensions under…

低秩张量的统计推断：异方差、次高斯性与应用AI 解读

In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly used algorithm for tensor singular value decomposition, we establish nonasymptotic distributional theory and study how to construct confidence regions and intervals for both the estimated singular vectors and the tensor entries in the…

矩阵时间序列 CP 因子模型的识别与估计AI 解读

We propose a new method for identifying and estimating the CP-factor models for matrix time series. Unlike the generalized eigenanalysis-based method (J. R. Stat. Soc. Ser. B. Stat. Methodol. 85 (2023) 127–148) for which the convergence rates of the associated estimators may suffer from small eigengaps as the asymptotic theory is based on some matrix perturbation analysis, the proposed new method enjoys faster convergence rates which are free from any eigengaps. It achieves…

高维 m-dependent 数据的双重归纳中心极限定理AI 解读

We derive novel and sharp high-dimensional Berry–Esseen bounds for the sum of m-dependent random vectors over the class of hyperrectangles exhibiting only a poly-logarithmic dependence in the dimension. Our results hold under minimal assumptions, such as nondegenerate covariances and finite third moments, and exhibit an optimal sample complexity of order m(q−1)/(q−2)/n. Aside from logarithmic terms, the resulting rates match the optimal rates established in the univariate…

Vecchia 高斯过程的概率与统计性质AI 解读

Gaussian Processes (GPs) are widely used to model dependencies in spatial statistics and machine learning. However, exact inference is computationally intractable for GP regression, with a time complexity of O(n3). The Vecchia approximation scales up computation by introducing sparsity into the spatial dependency structure, represented by a directed acyclic graph (DAG). Despite its practical popularity, this approach lacks rigorous theoretical foundations, and the choice of…

递归自适应分割估计的统计与计算权衡AI 解读

Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is computationally infeasible, these models are typically trained using greedy algorithms. Although effective in many cases, these algorithms have been empirically observed to get stuck at local optima. We explore this phenomenon in the…