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基于常微分方程的非线性混合效应模型的变分自编码器推断AI 解读

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions, likelihood-based inference via the stochastic approximation EM algorithm (SAEM) is widely used, but it relies on Markov Chain Monte-Carlo (MCMC) to approximate subject-specific posteriors. As model complexity increases or observations per…

通过元学习估计因果图不确定时的干预分布AI 解读

In scientific domains -- from biology to the social sciences -- many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observational data. However, observational data are often compatible with multiple…

植被绿度驱动因素的空间变量选择：面向 MODIS 植被指数AI 解读

Understanding how environmental drivers relate to vegetation condition motivates spatially varying regression models, but estimating a separate coefficient surface for every predictor can yield noisy patterns and poor interpretability when many predictors are irrelevant. Motivated by MODIS vegetation index studies, we examine predictors from spectral bands, productivity and energy fluxes, observation geometry, and land surface characteristics. Because these relationships…

作为生成回归变量的固定效应AI 解读

Many economic models feature moment conditions that involve latent variables. When the latent variables are individual fixed effects in an auxiliary panel data regression, we construct orthogonal moments that eliminate first-order bias induced by estimating the fixed effects. Machine Learning methods and Empirical Bayes methods can be used to improve the estimate of the nuisance parameters in the orthogonal moments. We establish a central limit theorem based on the…

AMP框架下基于Lasso统计量的经验贝叶斯变量选择AI 解读

The Lasso is one of the most ubiquitous methods for variable selection in high-dimensional linear regression and has been studied extensively under different regimes. In a particular asymptotic setup entailing $n/p\to \text{constant}$, an i.i.d.~Gaussian $X$ matrix and linear sparsity, \citet{su2017false} analyzed the Lasso selection path and presented negative results, showing that maintaining small levels of the false discovery proportion comes at a substantial cost in…

循证决策价值的估计AI 解读

In an era of data abundance, statistical evidence is increasingly critical for business and policy decisions. Yet, organizations lack empirical tools to assess the value of evidence-based decision making (EBDM), optimize statistical precision, and balance the costs of evidence-gathering strategies against their benefits. To tackle these challenges, this article introduces an empirical framework to estimate the value of EBDM and evaluate the return on investment in…

多元因果效应：贝叶斯因果回归因子模型AI 解读

The impact of wildfire smoke on air quality is a growing concern, contributing to air pollution through a complex mixture of chemical species with important implications for public health. While previous studies have primarily focused on its association with total particulate matter (PM2.5), the causal relationship between wildfire smoke and the chemical composition of PM2.5 remains largely unexplored. Exposure to these chemical mixtures plays a critical role in shaping…

ODDM 系统中基于分层稀疏贝叶斯学习的信道估计AI 解读

Orthogonal delay-Doppler division multiplexing (ODDM) is a promising modulation technique for reliable communications in high-mobility scenarios. However, the existing channel estimation frameworks for ODDM systems cannot achieve both high accuracy and low complexity simultaneously, due to the inherent coupling of delay and Doppler parameters. To address this problem, a two-dimensional (2D) hierarchical sparse Bayesian learning (HSBL) based channel estimation framework is…

高维 VAR 模型中的贝叶斯收缩：比较研究AI 解读

High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare three Bayesian shrinkage priors (horseshoe, lasso, and normal) and two frequentist regularization approaches (ridge and nonparametric shrinkage) under three carefully crafted simulation scenarios. These scenarios encompass (i) overfitting…

贝叶斯加性回归树的计算效率：渐近分析AI 解读

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory, comprising guarantees that its posterior distribution concentrates around the true regression function at optimal rates under various data generative settings and for appropriate prior choices. However, the computational properties of the…

边际似然函数的泛函估计AI 解读

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters. The method requires samples from the posterior distribution of the parameters for different values of the hyperparameters on a simulation grid and returns inference on the marginal likelihood defined everywhere on its domain, and on its…

条件异方差时间序列模型的稳健贝叶斯估计AI 解读

Outliers can seriously distort statistical inference by inducing excessive sensitivity in the likelihood function, thereby compromising the reliability of Bayesian estimation. To address this issue, we develop a robust Bayesian estimation method for conditionally heteroscedastic time series models by extending the density power divergence (DPD) framework to the Bayesian setting. The resulting DPD-based posterior distribution, controlled by a tuning parameter, achieves a…

数据整合中的经验贝叶斯方法AI 解读

We discuss the use of empirical Bayes for data integration, in the sense of transfer learning. Our main interest is in settings where one wishes to learn structure (e.g. feature selection) and one only has access to incomplete data from previous studies, such as summaries, estimates or lists of relevant features. We discuss differences between full Bayes and empirical Bayes, and develop a computational framework for the latter. We discuss how empirical Bayes attains…

稀疏泊松回归的变分推断AI 解读

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding conjugacy between the approximation component and the Gaussian prior on the regression coefficient. Three sparsity-enforcing priors (Laplace, Continuous Spike and Slab, and Bernoulli) are used for this problem. The proposed models are compared…

间歇参与下的预测综合：来自通胀密度调查的证据AI 解读

Central banks rely on density forecasts from professional surveys to assess inflation risks and communicate uncertainty. A central challenge in using these surveys is irregular participation: forecasters enter and exit, skip rounds, and reappear after long gaps. In the European Central Bank's Survey of Professional Forecasters, turnover and missingness vary substantially over time, causing the set of submitted predictions to change from quarter to quarter. Standard…

利用潜在干扰网络代理进行因果效应的贝叶斯估计AI 解读

Network interference occurs when treatments assigned to some units affect the outcomes of others. Traditional approaches often assume that the observed network correctly specifies the interference structure. However, in practice, researchers frequently only have access to proxy measurements of the interference network due to limitations in data collection or potential mismatches between measured networks and actual interference pathways. In this paper, we introduce a…

贝叶斯自助法中目标参数的后验不确定性AI 解读

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating equations. While much of the literature in Bayesian causal inference has relied on the conventional 'likelihood times prior' framework, a recently proposed method, the 'Linked Bayesian Bootstrap', deviated from this classical setting to obtain…

神经网络机器回归：揭示高阶协同效应的深度学习框架AI 解读

We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an end-to-end manner. By penalizing both gating parameters and redundant layers, NNMR yields sparse and interpretable architectures while capturing complex nonlinear relationships driven by high-order synergistic effects. We further develop a…

协方差与精度矩阵的高维 Bernstein-Von Mises 定理AI 解读

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis focuses on establishing asymptotic normality of the posterior distribution of the entire covariance/precision matrices under specific growth restrictions on $p_n$ and other mild assumptions. In particular, the limiting distribution turns out to…

基于熵正则化的扩展平均场变分推断：理论与计算AI 解读

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $Ξ$-variational inference ($Ξ$-VI). $Ξ$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $Ξ$-variational posteriors effectively…

集群随机交叉试验中存活者平均因果效应的贝叶斯方法AI 解读

In cluster-randomized crossover (CRXO) trials, groups of individuals are randomly assigned to two or more sequences of alternating treatments. Since clusters serve as their own control, the CRXO design is typically more statistically efficient than the usual parallel-arm design. CRXO trials are increasingly popular in many areas of health research where the number of available clusters is limited. Further, in trials among severely ill patients, researchers often want to…

策略行为主体的信息排序检验AI 解读

Specifying the information structure in strategic environments is difficult for empirical researchers. We develop a test of information ordering that examines whether the true information structure is at least as informative as a proposed baseline. Using Bayes Correlated Equilibrium (BCE), we translate the ordering of information structures into testable moment inequalities and establish uniform asymptotic validity for our testing procedure. In an application to U.S. airline…

面板数据预测：估计不确定性与参数异质性的权衡AI 解读

We provide a comprehensive examination of the predictive performance of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter…

面向相对数据的稳健函数型主成分分析AI 解读

This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been limited focus on developing robust methods to effectively handle anomalous observations and large noise. To address this, we extend the Mahalanobis distance concept to Bayes spaces, proposing its regularized version that accounts for the…