每日简报

正态均值估计中收缩阈值规则的近似风险最小化AI 解读

We develop an approximate risk minimization framework for shrinkage-thresholding estimation in normal mean problems. In the canonical multivariate normal mean model, we introduce a general functional class of estimators that contains classical shrinkage and thresholding behavior, including James-Stein-type and lasso-type rules. We express quadratic risk as a functional over this class, derive optimality conditions for both oracle risk and data-driven approximate risk…

MAPLE：基于 Mapper 的局部预测与数据驱动覆盖选择AI 解读

High dimensional biomedical data often exhibit nonlinear, heterogeneous, and manifold driven structures that challenge global parametric and tree-based models. We propose MAPLE (mapper-based Adaptive Prediction via Local Estimation), a localized prediction framework grounded in topological data analysis. The method is formulated as a nonparametric estimator of conditional class probabilities that adapts to the intrinsic geometry of the predictor space. Neighborhoods are…

暴露或结局罕见时哪种正则化倾向得分与双稳健方法校准最佳？基于代理混杂调整的plasmode研究AI 解读

Purpose. Confounding adjustment in health-care database studies screens large proxy libraries where events per variable are low, straining standard propensity score (PS) methods, and many regularized variable-selection strategies exist (outcome-adaptive LASSO [OAL], group LASSO/GLiDeR, highly adaptive LASSO [HAL]). Yet few comparisons have varied exposure prevalence within such a selection menu, and none pairs it with doubly robust estimation, compute accounting, and a…

从文本到参数：用嵌入正则化预测项目参数及其信度与设计上限AI 解读

Newly developed items must ordinarily be field tested before their psychometric properties are known, creating a cold start problem for item calibration. Predicting item parameters from features is a long standing measurement problem dating back to the Linear Logistic Test Model; modern text embeddings now automate the design matrices traditionally specified by hand. We propose an evaluation framework combining regularized regression on item text embeddings, repeated cross…

变分贝叶斯变量选择后的潜在结构恢复：部分探索性因子分析的拟合评估与因子数选择AI 解读

In partially exploratory factor analysis (PEFA), the loading structure and factor numbers are weakly specified. The regularized variational approximation for partially confirmatory factor analysis (PCFA VA) recovers this structure via Bayesian variable selection, using spike and slab priors to assign inclusion probabilities to unspecified loadings. This research introduces a post selection assessment framework for this approach. We convert converged solutions into covariance…

最小范数插值的局部Banach空间理论：高斯性的作用AI 解读

We study minimum-norm interpolation (MNI) in overparameterized linear regression with isotropic Gaussian covariates, in settings where the MNI has no closed-form formula. Whereas most prior work relied on Gaussian comparison tools such as the convex Gaussian min--max theorem (CGMT), our approach uses tools from high-dimensional geometry and probability. First, when the norm is in isotropic position, we obtain an ``offset'' bound that controls the amount by which the MNI…

比例高维下尺度混合误差的贝叶斯DAG结构学习与收缩协方差估计AI 解读

We propose a unified Bayesian framework namely robust DAG-Cholesky horseshoe (R-DACH) for joint directed acyclic graph (DAG) structure learning and precision matrix estimation in the high-dimensional proportional asymptotic regime $p/n \to c \in (0,\infty)$, under the scale mixture of normal errors. The construction places a global-local horseshoe-type prior directly on the strictly lower-triangular entries of the modified Cholesky factor of the DAG-Markov precision matrix,…

高维插值器可能脆弱：重尾与高维大偏差AI 解读

High-dimensional interpolation is common in modern machine learning, but its tail risk is less understood than its expected prediction risk. Existing theory shows that interpolating models can perform well in expectation, yet such guarantees do not determine the probability of rare, severe errors. In operations research and stochastic decision-making applications, rare estimation errors can have disproportionate downstream effects, so tail behavior matters alongside average…

面向分布型数据的动态Fréchet回归与特征选择AI 解读

Many scientific and engineering applications generate responses that are not scalars or vectors, but statistical objects whose form evolves over an ordered index such as time, depth. Probability distributions are a prominent example, capturing variability and uncertainty that cannot be summarized by low-dimensional statistics. When such responses are observed sequentially, the resulting dynamic distributional trajectories pose significant challenges for regression,…

空间模式的正则化估计AI 解读

Global warming and the El Niño phenomenon cause various climate changes and anomalies worldwide. Recently, extreme weather events such as heatwaves, droughts, and floods have become increasingly frequent. Researchers have studied atmospheric dynamics to reduce potential damage and increase safety. Statistical methods such as principal component analysis and maximum covariance analysis have been widely used to analyze spatial patterns of atmospheric variables. However, when…

基于似然的深度学习斑点回归的极小极大理论AI 解读

Speckle noise is a multiplicative noise commonly encountered in coherent imaging modalities such as synthetic aperture radar, optical coherence tomography, and digital holography. Although deep learning methods, in practice, have achieved state-of-the-art performance for speckle denoising, their fundamental statistical limits remain largely unexplored. Unlike additive noise models, multiplicative speckle noise makes the regression function unidentifiable from the conditional…

Copula 回归模型设定正确性的检验AI 解读

We propose a goodness-of-fit test for semiparametric copula regression models. Such models express the regression function in terms of marginal distribution functions and copula densities and therefore provide a flexible way to avoid fully nonparametric estimation in high-dimensional regression problems. Their performance, however, depends crucially on the specification of the parametric copula family. Instead of testing the copula model itself, we assess misspecification…

部分观测动态网络上的传染病过程完全数据似然AI 解读

Inference for infectious disease transmission on dynamic contact networks is complicated by latent infection times, partially observed network evolution, measurement error in contact data, and infection originating from outside the observed population. Existing likelihood-based approaches typically address these challenges separately and often rely on restrictive assumptions such as fully observed networks, closed populations, or symptom onset as a surrogate for infection…

线性与逻辑回归中的仅预测蒸馏AI 解读

Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime through a fresh-X prediction-mixed scheme: a pure-distilled student is trained on fresh covariates pseudo-labeled by the teacher, and the final…

经验空间分布函数的维度不变一致性与空间深度估计AI 解读

We provide a proof that the empirical spatial distribution estimator in $\mathbb R^d$ as well as the corresponding plug-in estimator of the spatial depth are uniformly $L^1$-consistent. The consistency rate only depends on the sample size $n$, not on the dimension $d$ or any tuning or regularization parameters. This is a rare property. The result of this note originates from a conversation with ChatGPT 5.4 Pro as part of some of our own earlier experiments on its…

去底主成分回归：仅靠秩选择不足以预测AI 解读

Principal component regression (PCR) regularizes high-dimensional prediction by choosing a spectral cutoff, but rank selection cannot correct systematic inflation of the retained empirical eigenvalues. We study clean Gaussian random designs in which the aggregate covariance tail creates a nearly scalar sample-space floor comparable to the predictive head scale. De-floored principal component regression (dPCR) retains the cutoff and subtracts an estimated floor from the…

在电子健康记录表型算法中使用二元银标签AI 解读

Gold-standard phenotype labels are often unavailable at scale in electronic health record (EHR) studies because they require manual chart review. Weakly supervised phenotyping methods instead use silver-standard labels, such as diagnosis-code counts, natural language processing (NLP) mentions, medication indicators, or laboratory thresholds. PheNorm is widely used for this purpose, but its original formulation was designed for count-valued silver labels and relies on log…

面向多模态协变量的平面曲线深度形状回归AI 解读

The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional…

重尾预测变量的球协差筛选AI 解读

High-dimensional screening is commonly built on covariance, correlation, or least-squares measures. These summary measures can be unstable or even undefined, when predictors are sparse or have heavy-tailed distributions. Building on our recent work on extended codifference and the idea of Ball-covariance, we develop Ball-codifference for marginal screening in statistical modeling with heavy-tailed predictors and responses. The proposed statistic combines the rank-type…

高维变点检测的椭圆正则化Hotelling检验AI 解读

We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and…

面向张量响应变量的一致特征筛选方法及其在全基因组面部形状关联中的应用AI 解读

As data collecting technologies advance, data structures are getting more and more complex, from single vectors to multi-dimensional tensors. This article is motivated by a variable selection problem to detect important genes from an ultrahigh dimensional pool that are associated with human facial shape variations. We propose a data-driven trimmed feature screening method based on a tensor ridge regression model (TrimTenRidge) through setting thresholds on the tensor…

超越负岭端点：经负移梯度下降的混合符号谱正则化AI 解读

In overparameterized linear regression, many weak spectral directions act like a ridge penalty on the signal-bearing spectrum; negative ridge is the natural correction, pushing filters above one. The stable negative-ridge endpoint, however, is structurally limited: its pole must stay below the smallest nonzero empirical eigenvalue, and it anti-shrinks smaller eigenvalues more than larger ones. Early-stopped negative-shifted gradient descent escapes this constraint. Its…

情境自适应推断：统计与基础模型的统一视角AI 解读

Modern predictive systems are expected to adapt their behavior to the specific situation they are facing. A clinical model should not treat every patient the same; a retrieval-augmented model should change its answer when given different evidence; a mixture-of-experts model should route different inputs to different experts. We call this capability context-adaptive inference: before predicting, the system uses information about the current context to specialize its…

共享支撑、异质边强度下的多精度矩阵估计AI 解读

Estimating multiple precision matrices in high-dimension presents significant challenges, particularly when distinct datasets share a common conditional dependency structure but exhibit population-specific interaction strengths. We address this problem by introducing the Multiplicative Graphical Lasso (Mglasso), a method for jointly estimating precision matrices across multiple Gaussian graphical models under a shared sparsity constraint. Each precision matrix is decomposed…