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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…

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…

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…

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…

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…

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…

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…

马尔可夫折棒过程AI 解读

Stick-breaking has a long history and is one of the most popular procedures for constructing random discrete distributions in statistics and machine learning. In particular, due to their intuitive construction and computational tractability they are ubiquitous in modern Bayesian nonparametric inference. Most widely used models, such as the Dirichlet and the Pitman–Yor processes, rely on i.i.d. or independent length variables. Here, we pursue a completely unexplored research…

利用最优传输构建多属性数据的Copula图模型AI 解读

Abstract Motivated by modern data types such as images and multi-view data, the multi-attribute graphical model aims to uncover conditional independence structures among vector-valued nodes. Under the Gaussian assumption, such independence is encoded in blockwise zeros of the precision matrix. To relax the restrictive Gaussian assumption, we propose a semiparametric multi-attribute graphical model leveraging a newly introduced cyclically monotone copula. This copula treats…

双重 LASSO：复现与实践启示AI 解读

ABSTRACT The rise of machine learning (ML) is one of the most prominent developments in applied econometrics in the past decade. The focus of much economic analysis is causal, rather than prediction, and Belloni et al. (2014) demonstrate how ML methods can be used in causal inference. This paper undertakes a narrow and wide replication of the Monte Carlo and empirical examples presented by Belloni et al. (2014). We discuss practical implications of this replication for the…

不完全依从的协变量自适应随机化中，利用回归调整提高估计效率AI 解读

Abstract We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust moment for local average treatment effects, are consistent and asymptotically normal even with heterogeneous probabilities of assignment and misspecified regression adjustments. We propose an optimal but potentially misspecified…

广义非参数模型中深度神经网络估计量的统计推断AI 解读

While deep neural networks (DNNs) are used for prediction, inference on DNN-estimated subject-specific means for categorical or exponential family outcomes remains underexplored. We address this by proposing a DNN estimator under generalized nonparametric regression models (GNRMs) and developing a rigorous inference framework. Unlike existing approaches that assume independence between estimation errors and inputs to establish the error bound, a condition often violated in…

结构动态离散选择模型的反事实分析AI 解读

Abstract Discrete choice data allow researchers to recover differences in utilities, but these differences may not suffice to identify policy-relevant counterfactuals of interest. In fact, in the case of dynamic discrete choice models, only a narrow set of counterfactuals are point-identified. In this paper, we explore how much one can learn about counterfactual outcomes of interest within this framework. We focus on the partial identification of counterfactuals, while…

高维混杂下条件平均处理效应的非参数估计AI 解读

SUMMARY This study considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties such as consistency,…

SUMMARY This paper extends difference-in-differences (DiD) to settings with continuous treatments. Specifically, the average treatment effect on the treated (ATT) at any level of treatment intensity is identified under a conditional parallel trends assumption. Estimating the ATT in this framework requires first estimating infinite-dimensional nuisance parameters, particularly the conditional density of the continuous treatment, which can introduce substantial bias. To…

二元结果高维广义线性模型中的因果推断AI 解读

Summary This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a single convex optimization that approximately balances link-derivative-weighted covariates and controls variance; it does not rely on estimated propensity scores. Under standard conditions, the estimator is $\sqrt{n}$-consistent…

强化学习变量选择的序贯 Knockoffs 方法AI 解读

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a…

面板回归模型的核范数正则化估计AI 解读

In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to…