每日简报

测量误差下的树聚合组成数据回归AI 解读

Compositional covariates in microbiome studies are often measured with error and organized by a biological hierarchy. Tree aggregation can improve multiresolution interpretation, but it also combines leaf-level errors into correlated contamination whose scale varies across the hierarchy. Existing tree aggregation and compositional measurement-error correction do not combine directly in redundant tree coordinates because a generic positive semidefinite projection can make the…

Wahkon：具有统计原则的深度RKHS叠加网络AI 解读

Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training…

误分类二元数据的贝叶斯分位数回归及配偶暴力报告应用AI 解读

Survey responses on socially undesirable behaviors, such as self-reported spousal violence, are often subject to underreporting due to social stigma, fear of retaliation, and other reporting pressures. When such data are analyzed using standard econometric models that focus on conditional means, such as probit and logit models, the resulting estimates are likely to be biased and can obscure heterogeneity in covariate effects. To address these challenges, we propose a…

不确定性来源的贝叶斯推断：从置信度建模到稀疏估计AI 解读

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and regularisation control. Building on this framework, we develop a general approach for inducing sparsity in statistical models and illustrate its use in linear and logistic regression, as well as in Bayesian neural networks.

动态藤Copula：检测与量化时变高阶交互AI 解读

Time-varying dependence is often modeled with dynamic correlations or Gaussian graphical models, but multivariate systems can change through tail behavior, asymmetry, or conditional structure even when correlations are nearly stable. We introduce Dynamic Vine Copulas (DVC), a temporal vine-copula framework for estimating and diagnosing sequence-wide non-Gaussian dependence. DVC fixes a chosen vine factorization for comparability; the framework applies to C-, D-, and R-vines,…

正则非光滑模型的归一化最大似然：测度论基础与几何采样AI 解读

The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework collapses for the non-smooth estimators ubiquitous in modern machine learning (e.g., Lasso, Sparse SVMs). In this work, we provide a rigorous framework for computing the NML for regular path-differentiable Lipschitz (PDL) estimators. By…

序贯二值模型中的实用边界退化与反向鞅极限AI 解读

A run of all failures, a run of all successes, or complete separation in a logistic regression each tempts the analyst to declare a probability of exactly zero or one. The central message of this paper is that all three phenomena share a common structure: finite sequential data justify practical boundary statements of the form $p\leq\varepsilon$ or $p\geq1-\varepsilon$, but not exact boundary probabilities. The paper's contribution is to unify these three settings under a…

遗憾与协方差：随机优化的闭式刻画AI 解读

Quantifying regret typically involves repeatedly re-solving a stochastic optimization problem across simulated scenarios. Such an approach is costly: the cost scales with the number of scenarios and the cost of each solve. We propose that regret can instead be measured using the joint moments of the cost vector $c$ and the optimal decision $π^*(c)$. Working with the optimal concave and Lipschitz under only a feasible region value function $v(c) = \min_{z\in Z} c^\top z$, we…

异质处理效应下工具变量方法的实用指南AI 解读

Instrumental variables (IV) methods are central to applied microeconomics. While classical approaches assume linear models with constant effects, recent literature has shifted toward the local average treatment effect (LATE) framework to accommodate heterogeneous treatment effects. This paper provides a practical guide to aligning empirical practice with recent theory. We first examine how different specifications with covariates lead to distinct weighted averages of…

空间依赖全局-局部收缩先验下的泊松回归区域选择与预测AI 解读

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence. Although standard variable selection approaches can help detect the sparse structure, incorporating the dependence into variable selection helps recover spatially contiguous signals and improves prediction accuracy. Motivated by a…

非凸稳健张量回归：算法与统计理论AI 解读

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression method for analyzing high-dimensional tensor data with heavy-tailed random noise. The proposed method is based on a nonconvex relaxation of the tensor tubal rank within a general optimization framework, which allows for nonconvexity in both…

面向混合健康结局的贝叶斯低秩潜类回归AI 解读

High-dimensional health and surveillance studies often involve many collinear predictors, multiple correlated outcomes of different types, and latent heterogeneity across observational units. We propose a Bayesian latent-cluster reduced-rank regression model for multivariate mixed outcomes. The model is a finite mixture of regression surfaces: each latent cluster has a cluster-specific mean shift and a low-rank coefficient matrix, yielding simultaneous clustering, dimension…

带线性结构的自适应核岭回归：尖锐 oracle 不等式与极小极大最优性AI 解读

Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal, instead applying a single functional regularization to the entire function. This may lead to unnecessary shrinkage of linear structure and consequently suboptimal prediction performance. In this paper, we propose a modified regression…

We consider the joint estimation of change-point locations and the sparsity pattern of the variance-covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change-point detection and covariance estimation accuracy. We establish the conditions…

空间适配器：冻结预测器的结构化空间分解与闭式协方差AI 解读

We present the Spatial Adapter, a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured spatial representation of its residual field and an induced closed-form spatial covariance. The adapter operates as a cascade second stage on residuals, jointly learning a spatially regularized orthonormal basis and per-sample scores via a tractable mini-batch ADMM procedure, without modifying any first-stage parameter. Because the first-stage…

集合滤波的数据一致性方法AI 解读

Ensemble filtering of chaotic, partially observed systems is often performed with ensembles far smaller than the state dimension resulting in empirical covariances that are low rank. Subsequently, stochastic observation perturbations can degrade both accuracy and probabilistic calibration. We develop a data-consistent perspective on ensemble filtering and introduce the Quantity-of-Interest Principal Component Analysis Ensemble Data Consistent Filter (QPCA-EnDCF), which is a…

拜占庭鲁棒分布式稀疏学习再审视AI 解读

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local $\ell_1$-regularized robust estimation with robust aggregation at the server, the framework applies to pseudo-Huber regression, quantile regression, and sparse SVM. We show that the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient. Simulations confirm…

相对稀疏性的自适应方差估计量AI 解读

An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients. Here, we develop a new coefficient variance estimator that fully uses this theorem and, in the process, takes into account the variable selection. This improves the uncertainty representation in the graphical selection diagrams, ultimately…

双稀疏正则化模型的近端投影方法AI 解读

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors can be represented by a Gaussian graphical model, the structure of the predictor graph can be exploited during regularization. Our proposed model exploits this underlying predictor graph structure by decomposing the estimated coefficient…

贝叶斯稀疏回归的谱塌缩 Gibbs 采样器AI 解读

Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone into speeding up the high-dimensional coefficient update step, insufficient attention has been given to the potential poor mixing of the global scale parameter $τ$ and of the overall sampler. One proposed remedy has been to marginalize out…

超越独立性：贝叶斯反演中的联合正态先验AI 解读

We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation terms that can be difficult to interpret statistically. We instead construct jointly Gaussian prior models with prescribed Gaussian marginals, so that correlation between the parameters can be incorporated without altering the marginal prior…

纵向函数对函数回归的高效推断AI 解读

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies…

具有时空结构的高维多元 VAR 估计AI 解读

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are observed over many spatial locations. This paper develops a structured estimation procedure for high-dimensional multivariate VAR processes that explicitly incorporates spatial information. We decompose each block transition matrix into a…

高维平滑支持向量机的统计推断：从离线到在线数据AI 解读

High-dimensional classification problems often rely on the Lasso-penalized linear Support Vector Machines (SVMs). However, the double non-smoothness induced by the hinge loss and Lasso penalty in this model makes statistical inference challenging and impedes computational efficiency. In this paper, we propose a unified inference framework in both offline and online settings. In the offline case, by applying a convolution smoothing technique to the hinge loss, we construct a…