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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…

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…

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…

有向网络互惠效应的最优估计与检验AI 解读

The $p_1$ model plays a fundamental role in modeling directed networks, where the reciprocal effect parameter $ρ$ is of special interest in practice. However, due to nonlinear factors in this model, how to estimate $ρ$ efficiently is a long-standing open problem. We tackle the problem by the cycle count approach. The challenge is, due to the nonlinear factors in the model, for any given type of generalized cycles, the expected count is a complicated function of many…

似然模型中附带参数问题的 Neyman 正交化方法AI 解读

A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is zero. Such first-order orthogonalization allows the estimator of the nuisance parameters to converge at a slower-than-parametric rate. It may, however, not suffice when the nuisance parameters are very imprecisely estimated. Leading…

基于最优传输的贝叶斯后验采样生成模型AI 解读

Abstract We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Building on transport map-based generative models for posterior sampling, we propose an optimal transport (OT)-constrained transport map class that learns a deterministic map from a reference distribution to the target posterior through constrained optimization. The proposed class exploits structural properties of OT maps and allows…

重新审视石油供给新闻冲击：代理变量与非高斯结构向量自回归AI 解读

ABSTRACT We replicate a study by Känzig ( American Economic Review , 111 (2021), 1092–1125), who employs structural vector autoregressive techniques to examine the impact of changes in oil supply expectations on the price of oil and other macroeconomic aggregates. Känzig identifies an oil supply news shock by constructing a proxy from OPEC announcements about their production plans. As an alternative approach, we use non‐Gaussianity and independence to identify structural…

大冲击宏观模型的快速高效估计AI 解读

We propose a new approach for efficiently estimating and analyzing macroeconomic models subject to large shocks. We apply the methodology to a two-sector model that captures the heterogeneous exposure of different sectors to the COVID-19 pandemic. We solve the model nonlinearly and propose a new nonlinear, non-Gaussian filter designed to handle large shocks and identify their source and time location. Monte Carlo experiments show that the estimation and identification of…

对 Suri (2011)《技术采纳中的选择与比较优势》的评论AI 解读

This paper illustrates and addresses weak identification in the correlated random coefficient (CRC) model that Suri (2011) uses to study agricultural technology adoption. Using the publicly available dataset, which differs slightly from the version used in Suri (2011), we obtain different point estimates for the paper’s main CRC model. To understand why these differences are as large as they are, we recast the CRC model as a more general random coefficient model in which the…

协变量漂移下外部有效性的简单稳健性度量AI 解读

This paper studies the robustness of estimated policy effects to changes in the distribution of covariates, a key determinant of the external validity of (quasi)experimental results. I propose a novel robustness metric δ ∗ which measures the smallest covariate shift needed to invalidate an empirical claim about the policy effect (e.g., AT E > 0). I estimate δ ∗ via de-biased GMM, achieving a parametric rate of convergence while accommodating machine-learning estimators of…

一个精确 t 检验AI 解读

Multivariate linear regression and randomization-based inference are two essential methods in statistics and econometrics. Nevertheless, the problem of producing a randomized test for the value of a single regression coefficient that is exactly valid when errors are exchangeable, and which is asymptotically valid for the best linear predictor, has remained elusive. In this paper, we produce a test that is exactly valid with exchangeable errors and which allows for general…

从预测算法到异常的自动生成AI 解读

How can we extract theoretical insights from machine learning algorithms? We take a familiar lesson: researchers often turn intuition into theoretical insight by constructing “anomalies” — specific examples highlighting hypothesized flaws in a theory, such as the Allais paradox. We develop procedures that replace researchers’ intuitions with predictive algorithms: given a predictive algorithm and a theory, our procedures automatically generate anomalies for that theory. We…

异质性主体下的极值理论AI 解读

Extreme value processes feature in any economic model in which agents receive a number of draws from some distribution and we examine the behavior of the maximum in the limit as the number of draws becomes large. This paper asks: Do the average outcomes of such processes change when different agents receive a different number of draws? To answer this, we allow the number of draws an agent receives from the underlying distribution (e.g. of productivities, ideas, or utility…

集合值预测与模型误设下的信息推断AI 解读

This paper proposes an information-based inference method for partially identified parameters in incomplete models that is valid both when the model is correctly specified and when it is misspecified. Key features of the method are: (i) it is based on minimizing a suitably defined Kullback-Leibler information criterion that accounts for incompleteness of the model and delivers a non-empty pseudotrue set; (ii) it is computationally tractable; (iii) its implementation is the…

最富者为何如此富有？新的纵向经验证据及其对财富不平等理论的启示AI 解读

We study the lifecycle dynamics of wealth inequality using 1993-2019 Norwegian administrative panel data on wealth and income. Employing a novel budget-constraint approach, we decompose the excess wealth of the top 0.1% households relative to the median between ages 45 and 64 into higher saving rates (36%), inheritances (31%), returns (28%), and labor income (5%). One-quarter of the wealthiest—the “New Money”—start with negative wealth on average but accumulate rapidly…