每日简报

非线性观测下实例最优的稀疏恢复：统一框架AI 解读

This paper develops a unified framework for instance optimal sparse recovery from nonlinear observations. The main ingredient is a signal-dependent restricted approximate invertibility condition (RAIC) of some gradient, which leads to the instance optimality of iterative hard thresholding. Under Gaussian designs, we apply the proposed framework to phaseless, one-bit, and ReLU measurements, which correspond to the problems of sparse phase retrieval, one-bit compressed…

基于极值分布的高斯图模型自适应正则化AI 解读

Edge selection in Gaussian graphical models is fundamentally a variable selection problem where pairwise relationships determine construct validity and variable importance in psychological networks. In psychology, network estimation relies predominantly on \(\ell_1\) regularization where uniform shrinkage systematically underestimates edge and centrality parameters. Alternative penalties overcome this bias but rely on fixed hyperparameters that do not adapt to the signal in…

动态空间贝叶斯机器学习：美国代际流动与地理收入不平等应用AI 解读

We develop a Dynamic Spatial Panel Bayesian Additive Regression Trees model with Horseshoe shrinkage (DSP-BART-HS) for high-dimensional spatio-temporal panel data. We jointly evaluate the model against a comprehensive suite of structural spatial econometrics, non-parametric machine learning methods, and small-area estimators across nine data-generating scenarios spanning 200 replicates each, including irregular spatial topologies, dense policy effects, and non-linear…

超越受限等距性质的低秩矩阵恢复优化景观：秩一测量应用AI 解读

We study the problem of low-rank matrix recovery from linear measurements via the global nonconvex landscape of a low-rank factored formulation of the matrix LASSO (nuclear-norm--regularized least-squares). If the landscape is benign, that is, has no bad local optima, then practical and scalable algorithms can compute good statistical estimates. Previous state-of-the-art landscape guarantees have typically assumed that the linear measurement operator has the restricted…

收缩使 Hosmer–Lemeshow 检验失效：惩罚逻辑回归拟合优度及青光眼应用AI 解读

Clinical prediction models are increasingly fitted by penalized logistic regression, because collinearity or many candidate predictors makes maximum likelihood unstable or impossible. Calibration is then almost always assessed by a grouped goodness-of-fit test such as the Hosmer-Lemeshow test. We show that this combination is invalid. Under ridge regression the grouped standardized residuals acquire a non-centrality induced by shrinkage, so the reference distribution used in…

基于结构信息的迁移学习AI 解读

Transfer learning improves estimation in a target study using information from related sources. Classical transfer learning is typically data-based, requiring access to the source data or to a model fitted on them. Neither is available in many modern studies, as both are often proprietary or unreported. What can be transferred instead is structure: summarized information derived from a source, such as the supports of predictors, which is available and interpretable without…

异质特征空间下线性回归的迁移学习AI 解读

Transfer learning improves target-task performance by leveraging related source data. Most methods assume shared feature spaces, yet in many applications, each source observes only a subset of target covariates. Classical imputation fails here due to block missingness, and standard imputation matrices are not optimized for target parameter estimation. We study low- and high-dimensional linear regression and propose Heterogeneous Importance Weighting (HIW). Our method aligns…

Lipschitz 谱算法下 RKHS 回归与序列模型的风险等价AI 解读

Kernel spectral algorithms are often summarized by convergence rates, which hide how their risk depends jointly on regularization, noise, the population spectrum, target coefficients, and the chosen filter. Gaussian sequence models arise as a simplified but characteristic setting for studying the interplay of these factors, where the kernel spectral algorithm corresponds to a coordinatewise shrinkage estimator. Under mild assumptions, we show that the risk of a kernel…

低温下的高磁化采样：Ising模型与贝叶斯稀疏线性回归AI 解读

Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over the Hamming slice $\mathcal{X}_k^d:=\{\mathbf{x}\in\{\pm 1\}^d:|\{i:\mathbf{x}_i=1\}|=k\}$, in high-dimensional regimes where $k\ll d$ (i.e., where $\mathcal{X}_k^d$ is \emph{highly magnetized}). We use our frameworks to design improved samplers for canonical problems in the study of \emph{Ising models} and \emph{Bayesian sparse…

稀疏正则化多边际最优传输与重心的中心极限定理及自助法AI 解读

Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic…

心理测量结局缺失时高维预测变量的贝叶斯选择AI 解读

High-dimensional, multimodal predictors and partially observed multivariate outcomes are common in psychometric research. However, existing regularization methods often do not accommodate hierarchical predictor structures and are primarily designed for univariate outcomes. We propose SHIM, a Bayesian framework for structured variable selection that combines hierarchical horseshoe shrinkage with a Bayesian treatment of missing outcomes. The framework jointly accommodates…

比例高维线性模型中的最优线性泛函估计AI 解读

We study estimation of a linear functional in random-design linear models when $γ=p/n \in (1, \infty)$ under the dense regime where the design covariance is unknown, and neither the regression vector nor the precision matrix is assumed sparse. Suppose the spectrum of the design covariance belongs to $[\ell,L]$, we establish the minimax mean squared rate for the linear functional has the order $n^{-α(κ,γ)}$, where the exponent $α(κ,γ)$ has an explicit elliptic-integral…

设计信息辅助的回归AI 解读

We consider regression problems in which the marginal distribution of the covariates is informative for estimation and variable selection, rather than merely auxiliary. Motivated by random-design, high-dimensional, and latent-effect settings, we propose a general design-assisted regression framework in which the estimating criterion depends on both the conditional model for $Y \mid \bfX$ and structured features of the covariate distribution. The framework identifies two…

有限混合回归模型的分量加权稀疏组 LASSOAI 解读

When analyzing heterogeneous data with latent subpopulations, finite mixture regression (FMR) models are effective as they allow for variations in regression coefficients across mixture components. Variable selection is important at two levels: (1) at the group level by removing completely irrelevant covariates across all subpopulations and (2) at the individual level by removing irrelevant covariates within each subpopulation. However, existing variable selection methods…

Banach 空间中含测量误差的非参数回归AI 解读

We consider nonparametric regression with a Banach-space-valued predictor where the covariate takes values in a general separable Banach space. Our primary objective is to develop a unified framework for estimating the regression operator without relying on an inner-product structure, thereby extending classical and functional nonparametric regression beyond Euclidean and Hilbert spaces in the presence of measurement error. We establish the fundamental properties of the…

非欧几里得响应的抗多重共线性特征筛选：因子调整方法AI 解读

In high-dimensional settings, multicollinearity is a pervasive issue that can substantially impair the performance of feature screening methods based on marginal Fréchet regression. Feature screening for non-Euclidean responses becomes unreliable when ultrahigh-dimensional predictors suffer from multicollinearity, because feature-specific signals may be masked by shared latent factors. To mitigate this effect, we propose a Factor adjusted Fréchet sure independence screening…

惩罚变换分布回归：兼顾可解释性与协变量依赖的形状灵活性AI 解读

A central challenge in distributional regression is to allow the shape of the conditional distribution of the response variable to vary flexibly with covariates while retaining directly interpretable effects on its mean and standard deviation. We extend the penalized transformation model (PTM) family into a conditional-shape PTM, which assigns separate structured additive predictors to the conditional mean, standard deviation, and standardized distributional shape beyond…

布尔超立方体上的可分辨傅里叶阶数与极小极大估计AI 解读

We study high-dimensional nonparametric regression on the Boolean hypercube \(\{0,1\}^d\), from a sample of size \(n\), under a Fourier--Sobolev budget, i.e., a bound \(B\) on the total quadratic influence of the regression function. The central object is the resolvable Fourier degree \(D^*(d,n)\), defined as the largest interaction order \(D\) such that the dimension of the degree-\(D\) Fourier--Walsh space does not exceed \(n\). We prove that the minimax risk over…

Lévy 噪声下广义朗之万方程的历史条件化记忆与随机驱动推断AI 解读

We consider the identification of memory and stochastic forcing in a one-dimensional generalized Langevin equation with state-dependent Brownian noise and optional additive symmetric $α$-stable jumps. A finite-dimensional Markov embedding provides Kramers--Moyal conditional moment relations that separate memory drift, Brownian diffusion, and jump contributions. From increment ensembles conditioned on the observed velocity history, truncated statistics estimate the stable…

未知高斯噪声下的流形假说：条件性证书与一致维数估计AI 解读

We study what noisy data can establish about the Manifold Hypothesis under explicit identification and regularity conditions. A population residual certificate combines independent-view localization, Gaussian concentration, membership uncertainty, and population transfer. Existing rectifiability criteria then yield a covered-scale consequence. For a local smooth manifold with positive Hölder density, the actual-ball covariance limit identifies the spectral crossing with…

自助集成鞅后验：预测重采样的不确定性校准AI 解读

Martingale posteriors and related predictive resampling methods replace the likelihood--prior pair used within Bayesian inference with a predictive model for future observations. These methods are simple to implement and increasingly popular due to their computational efficiency, but little is known about their ability to accurately quantify uncertainty. In this work, we study the concentration and calibration properties of the martingale posterior for general functionals,…

蝾螈视网膜神经节细胞动态感受野的结构化贝叶斯建模AI 解读

Neurons in the visual system are selective for specific spatial and temporal stimulus features, described by their \emph{receptive field}. Estimating one means a coefficient per pixel per time bin from few trials -- a high-dimensional problem requiring regularization. Sparse regularizers such as the LASSO handle the dimension but select pixels independently at each time point, with nothing to keep the region coherent in space or smooth in time; it can fragment or reorganize…

高维多输出回归的联合稀疏迁移学习AI 解读

Multitask linear models can improve estimation and prediction by exploiting structure shared across responses, bridging taskwise fitting and complete pooling. In many applications, however, the objective is estimation in a data-limited target domain, while data-rich but heterogeneous source domains are available. Borrowing from these sources can improve efficiency but introduce bias. We develop a joint-sparse transfer-learning framework for high-dimensional multi-output…

预测变量相关下基于自适应虚拟变量的可扩展变量选择AI 解读

Reliable high-dimensional variable selection requires scalable error-controlling methods. The Terminating-Random Experiments (T-Rex) selector estimates the false discovery rate (FDR) by aggregating early-terminated forward-selection paths in which predictors compete with synthetic dummies. We address two remaining challenges: i) predictor dependence can bias dummy-predictor competition; ii) computation is wasted on recomputing terms shared across experiments. Building on…