每日简报

数据增强的高斯与非高斯普适性AI 解读

We provide universality results that quantify how data augmentation affects the variance and limiting distribution of estimates through simple surrogates, and analyze several specific models in detail. The results confirm some observations made in machine learning practice, but also lead to unexpected findings: Data augmentation may increase rather than decrease the uncertainty of estimates, such as the empirical prediction risk. It can act as a regularizer, but fails to do…

高维噪声下的广义稳健自适应带宽多视图流形学习AI 解读

Multiview datasets are common in scientific and engineering applications, yet existing fusion methods offer limited theoretical guarantees, particularly in the presence of heterogeneous and high-dimensional noise. We propose Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM), a new kernel-based diffusion geometry framework for integrating multiple noisy data sources. The key innovation of GRAB-MDM is a view-dependent bandwidth selection strategy that…

交叉设计的因果效应、有效估计与稳健推断AI 解读

Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both instantaneous effects of current treatments and carryover effects from past treatments. They are widely used in traditional biomedical studies and are increasingly adopted in modern digital platforms. However, standard analyses of crossover designs…

基于张量收缩的高维张量信号对齐与匹配检验AI 解读

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and the lack of suitable test statistics. By exploiting a recent tensor contraction method, we propose and validate relevant test statistics using eigenvalues of a data matrix resulting from the tensor contraction. The matrix entries exhibit…

SIMPLE-RC：非尖锐原假设与弱信号下的群组网络推断AI 解读

Large-scale network inference with uncertainty quantification has important applications in natural, social and medical sciences. The recent work of Fan et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 84 (2022) 630–653) introduced a general framework of statistical inference on membership profiles in large networks (SIMPLE) for testing the sharp null hypothesis that a pair of given nodes share the same membership profile. In real applications, there are often groups of…

神经网络雅可比矩阵的谱渐近：收敛、普适性与相变AI 解读

We study the spectral properties of the Jacobian matrix in artificial neural networks and establish both its limiting spectral distribution and the second-order fluctuations of its spectrum. Our analysis uncovers fundamental phenomena, including universality properties with respect to the weight distribution and a phase transition in spectral behavior driven by the choice of activation function. Leveraging tools from random matrix theory, we first analyze a class of…

基于预测生成树方法的贝叶斯空间区域划分一致估计AI 解读

Bayesian model-based spatial clustering methods are widely used for their flexibility in estimating latent clusters with an unknown number of clusters while accounting for spatial proximity. Many existing methods are designed for clustering finite spatial units, limiting their ability to make predictions or may impose restrictive geometric constraints on the shapes of subregions. Furthermore, the posterior clustering consistency theory of spatial clustering models remains…

空间混杂下高斯随机场回归斜率的填充渐近一致可估性AI 解读

The problem of estimating the slope parameter in regression between two spatial processes under confounding by an unmeasured spatial process has received widespread attention in the recent statistical literature. Yet, a fundamental question remains unresolved: when is this slope consistently estimable under spatial confounding, with existing insights being largely empirical or estimator-specific. In this manuscript, we characterize conditions for consistent estimability of…

流形上的粒度平滑AI 解读

Given a random sample from a density function supported on a manifold M, a new method for the estimating highest density regions of the underlying population is introduced. The new proposal is based on the empirical version of the opening operator from mathematical morphology combined with a preliminary estimator of the density function. This results in an estimator that is easy-to-compute since it simply consists of a list of centers and a radius r that are adequately…

二维 Navier–Stokes 方程的数据同化：后验测度的最优高斯渐近性质AI 解读

A functional Bernstein–von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier–Stokes equation where a Gaussian process prior is assigned to the initial condition of the system. The posterior measure, which provides the update in the space of all trajectories arising from a discrete sample of the (deterministic) dynamics, is shown to be approximated by a Gaussian random vector field obtained as the solution to…

半收缩漂移分数布朗运动驱动随机微分方程的平稳密度快速估计AI 解读

We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter H∈(0,1). We first focus on continuous observations and develop a kernel-based estimator achieving faster convergence rates than previously available. This result stems from a martingale decomposition combined with new bounds on the (conditional) convergence in total variation to equilibrium of fractional SDEs. For H<1/2, we further refine the rates…

基于抛物型Monge–Ampère偏微分方程的无遗憾生成建模AI 解读

We introduce a novel generative modeling framework based on a discretized parabolic Monge–Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. Our method performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. We establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map…

从杀死扩散过程推断扩散率AI 解读

We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given “binding potential.” The binding process can be modeled by an additive random functional corresponding to the canonical construction of a “killed” diffusion Markov process. We study the problem of conducting inference on the infinite-dimensional diffusion parameter…

异质性调整下分布式精度矩阵的最优整合估计AI 解读

Distributed learning offers a practical solution for the integrative analysis of multisource datasets, especially under privacy or communication constraints. However, addressing prospective distributional heterogeneity and ensuring communication efficiency pose significant challenges on distributed statistical analysis. In this article we focus on integrative estimation of distributed heterogeneous precision matrices, a crucial task related to joint precision matrix…

基于最近邻图的两样本检验的功效性质AI 解读

In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using interpoint distances. So far, the asymptotic theory of these tests applies only to graphs, which fall under the stabilizing graphs framework of Penrose and Yukich (Ann. Appl. Probab. 13 (2003) 277–303). We study the case of the K-nearest neighbors graph where K=kN increases with the sample size,…

使用 AI 学习表征的实用双重机器学习AI 解读

Text, images, and other rich covariates are increasingly compressed into AI-learned representations and then used as controls in causal analysis. We study when this approach is valid and develop a practical framework for causal inference with learned representations. For a broad class of estimands, an imperfect representation distorts the target causal parameter by the product of two representation errors: one in the outcome regression and one in the balancing weight (or…

We develop the first empirically implementable selective-inference framework for difference-in-differences with controls selected by pre-treatment fit. We construct confidence intervals for the average treatment effect on the treated (ATT), incorporating that selection and estimating the unknown full covariance from the same observations. Counterexamples establish undercoverage from Roth's fixed-comparison pretest adjustment and direct Gaussian-score application of…

随机正规算子近似下Landweber迭代的不确定性量化AI 解读

Iterative methods are extremely popular for solving linear ill-posed inverse problems. While deterministic convergence, or more precisely, semi-convergence of such methods is widely studied, the problem of quantifying uncertainty in the resulting reconstructions due to random noise in the observed data has received far less attention. In this work, we study uncertainty quantification for the Landweber iteration in linear inverse problems using the Radon transform as a…

函数型解释变量含测量误差的标量对函数回归AI 解读

We consider the problem of scalar-on-function regression. Most existing methods implicitly assume that the functional covariates are observed exactly, but in practice, they are often contaminated by measurement error. Our goal, therefore, is to deal with the problem of scalar-on-function regression when the regressor functions are observed with error. In this paper, we propose a simulation-extrapolation method to correct for the attenuation of estimated coefficient functions…

多源整合因子模型中共同与个体成分的检验及分离AI 解读

Disentangling shared (joint) structures from source-specific (individual) variations is a fundamental task in multi-source data integration. Existing joint-individual models often rely on computationally intensive optimization or loose spectral bounds, leading to suboptimal separation accuracy and poor scalability. In this paper, we propose the Multi-Source Sequential Alignment Test (MSSAT). MSSAT leverages the geometric observation that true joint components manifest as…

利用补充样本识别面板条件化：锐界与设计假设AI 解读

Refreshment samples are the standard remedy for panel attrition, and the identification results behind them maintain that participation does not change measurement. We characterize what a refreshment sample identifies about panel conditioning, modelled as a deterministic monotone map at reinterview, when attrition is unrestricted. A candidate map is consistent with the data if and only if the retention-scaled distribution of the stayers' implied latent outcomes is setwise…

期望效用遗憾规则：极小极大与贝叶斯最优投资组合选择AI 解读

This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and…

利用路径签名回归进行即时预测AI 解读

We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observations in continuous time, they naturally handle mixed frequencies and missing data. We prove theoretically, and demonstrate with simulations, that regression on signatures both subsumes the linear Kalman filter and has desirable consistency properties. Nowcasting with signatures is more robust to…

Wearable devices for continuous electronic health monitoring often capture data at frequent intervals under a dense functional design. The focal point is the analysis of longitudinal functional data, wherein functional trajectories are observed repeatedly over time. This work is motivated by the interest in assessing the efficacy of a noninflammatory medication, meloxicam, on the daily activity levels of household cats with a pre-existing condition of osteoarthritis under a…