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过参数化下的模型坍缩防范：插值学习与岭回归的最优混合比例AI 解读

Model collapse occurs when generative models degrade after repeatedly training on their own synthetic outputs. We study this effect in overparameterized linear regression in a setting where each iteration mixes fresh real labels with synthetic labels drawn from the model fitted in the previous iteration. We derive precise generalization error formulae for minimum-$\ell_2$-norm interpolation and ridge regression under this iterative scheme. Our analysis reveals intriguing…

Renet：通过动态目标选择为弹性网提供有原则且高效的松弛方法AI 解读

We introduce Renet, a principled generalization of the Relaxed Lasso to the Elastic Net family of estimators. While, on the one hand, $\ell_1$-regularization is a standard tool for variable selection in high-dimensional regimes and, on the other hand, the $\ell_2$ penalty provides stability and solution uniqueness through strict convexity, the standard Elastic Net nevertheless suffers from shrinkage bias that frequently yields suboptimal prediction accuracy. We propose to…

分布型工具变量：识别与分位数最小二乘估计AI 解读

We study instrumental-variable designs where policy reforms strongly shift the distribution of an endogenous variable but only weakly move its mean. We formalize this by introducing distributional relevance: instruments may be purely distributional. Within a triangular model, distributional relevance suffices for nonparametric identification of average structural effects via a control function. We then propose Quantile Least Squares (Q-LS), which aggregates conditional…

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…

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…

两阶段数据合成：隐私与预测之间由统计驱动的受限权衡AI 解读

Synthetic data have gained increasing attention across various domains, with a growing emphasis on their performance in downstream prediction tasks. However, most existing synthesis strategies focus on maintaining statistical information. Although some studies address prediction performance guarantees, their single-stage synthesis designs make it challenging to balance the privacy requirements that necessitate significant perturbations and the prediction performance that is…

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…

高维重尾局部平稳时间序列的稀疏学习：集中与预言不等式AI 解读

Sparse learning is ubiquitous in many machine learning tasks. It aims to regularize the goodness-of-fit objective by adding a penalty term to encode structural constraints on the model parameters. In this paper, we develop a flexible sparse learning framework tailored to high-dimensional heavy-tailed locally stationary time series (LSTS). The data-generating mechanism incorporates a regression function that changes smoothly over time and is observed under noise belonging to…

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…

Cox 模型变量选择后的统计推断：一项模拟研究AI 解读

Choosing relevant predictors is central to the analysis of biomedical time-to-event data. Classical frequentist inference, however, presumes that the set of covariates is fixed in advance and does not account for data-driven variable selection. As a consequence, naive post-selection inference may be biased and misleading. In right-censored survival settings, these issues may be further exacerbated by the additional uncertainty induced by censoring. We investigate several…

球面数据的 Monge-Kantorovich 分位数正则化估计AI 解读

Tools from optimal transport (OT) theory have recently been used to define a notion of quantile function for directional data. In practice, regularization is mandatory for applications that require out-of-sample estimates. To this end, we introduce a regularized estimator built from entropic optimal transport, by extending the definition of the entropic map to the spherical setting. We propose a stochastic algorithm to directly solve a continuous OT problem between the…

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…

AdapDISCOM：面向块状缺失与测量误差的高维多模态自适应稀疏回归AI 解读

Multimodal high-dimensional data are increasingly prevalent in biomedical research, yet they are often compromised by block-wise missingness and measurement errors, posing significant challenges for statistical inference and prediction. We propose AdapDISCOM, a novel adaptive direct sparse regression method that simultaneously addresses these two pervasive issues. Building on the DISCOM framework, AdapDISCOM introduces modality-specific weighting schemes to account for…

稀疏网络联合潜空间建模中的协变量选择AI 解读

Network data are increasingly common in the social sciences and infectious disease epidemiology. Analyses often link network structure to node-level covariates, but existing methods falter with sparse networks and high-dimensional node features. We propose a joint latent space modeling framework for sparse networks with high-dimensional binary node covariates that performs covariate selection while accounting for uncertainty in estimated latent positions. Building on joint…

非可加损失下不可共享数据的分布式卷积秩回归AI 解读

We study high-dimensional rank regression when data are distributed across multiple machines and the loss is a non-additive U-statistic, as in convoluted rank regression (CRR). Classical communication-efficient surrogate likelihood (CSL) methods crucially rely on the additivity of the empirical loss and therefore break down for CRR, whose global loss couples all sample pairs across machines. We propose a distributed convoluted rank regression (DCRR) framework that constructs…

基于变分稳定Doob匹配的扩散模型推理时对齐AI 解读

Inference-time alignment for diffusion models aims to adapt a pre-trained reference diffusion model toward a target distribution without retraining the reference score network, thereby preserving the generative capacity of the reference model while enforcing desired properties at the inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce variationally…

基于张量数据的扩散指数预测AI 解读

In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the…

用约束线性回归估计混合分位数AI 解读

We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its parameters, estimation reduces to constrained linear regression, yielding a convex optimization problem that readily accommodates cardinality constraints as well as L1 or smoothness regularization. For Lq-type objectives we show the…

神经熵正则最优传输与 Gromov-Wasserstein 对齐AI 解读

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs. Entropic regularization has emerged as a promising solution, allowing parametric convergence rates via the plug-in estimator, which can be computed using the Sinkhorn algorithm (or its iterations in the GW case). However, Sinkhorn's $O(n^2)$ time…

决策导向的最优传输AI 解读

We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective coefficients are random and may follow two distinct distributions. Traditional metrics such as KL divergence and Wasserstein distance are not well-suited for quantifying the resulting cost discrepancy, because changes in the coefficient distribution…

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…

预测石油消费：世界能源统计与机器学习的结合AI 解读

This paper studies whether a small set of dominant countries can account for most of the dynamics of regional oil demand and improve forecasting performance. We focus on dominant drivers within the OECD and a broad GVAR sample covering over 90\% of world GDP. Our approach identifies dominant drivers from a high-dimensional concentration matrix estimated row by row using two complementary variable-selection methods, LASSO and the one-covariate-at-a-time multiple testing…

交叉验证中的最优留出规模AI 解读

Cross-validation (CV) is routinely used across the sciences to select models and tune parameters, and the resulting choices are often interpreted as substantive scientific conclusions (e.g., which variables, mechanisms, or risk factors are ``supported by the data''). A key part of the CV procedure -- the hold-out size, or equivalently the fold count $K$ -- is typically set by convention (e.g., 80/20, $K=5$) rather than by a principled criterion. Central to the issue is the…