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基于变换L1正则化的含噪低秩矩阵补全及其理论性质AI 解读

This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1), which interpolates between the rank and the nuclear norm of matrices through a hyper-parameter $a \in (0, \infty)$. While some literature adopts such regularization for matrix completion, it primarily addresses scenarios with uniformly…

高维加速失效时间模型的迭代变量选择AI 解读

We propose an iterative variable selection method for the accelerated failure time model using high-dimensional survival data. Our method pioneers the use of the recently proposed structured screen-and-select framework for survival analysis. We use the marginal utility as the measure of association to inform the structured screening process. For the selection steps, we use Bayesian model selection based on non-local priors. We compare the proposed method with a few…

贝叶斯惩罚经验似然与马尔可夫链蒙特卡洛抽样AI 解读

In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the…

广义拉普拉斯矩阵潜在嵌入的特征向量渐近理论AI 解读

Laplacian matrices are commonly employed in many real applications, encoding the underlying latent structural information such as graphs and manifolds. The use of the normalization terms naturally gives rise to random matrices with dependency. It is well-known that dependency is a major bottleneck of new random matrix theory (RMT) developments. To this end, in this paper, we formally introduce a class of generalized (and regularized) Laplacian matrices, which contains the…

动态信息借用的渐近推断AI 解读

Large sample behavior of dynamic information borrowing (DIB) estimators is investigated. Asymptotic properties of several DIB approaches (adaptive risk minimization, adaptive LASSO, Bayesian procedures with empirical power prior, fully Bayesian procedures, and a Bayes-frequentist compromise) are explored against shrinking to zero alternatives. As shown theoretically and with simulations, local asymptotic distributions of DIB estimators are often non-normal. A simple Gaussian…

贝叶斯稳定性选择与选择概率推断AI 解读

Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates Bayesian analysis to refine the inference of selection probabilities within the stability selection framework. Traditional approaches rely on selection frequencies for decision-making, often disregarding domain-specific knowledge. Our…

时间序列数据的高维 Knockoffs 推断AI 解读

We make some initial attempt to establish the theoretical and methodological foundation for the model-X knockoffs inference for time series data. We suggest the method of time series knockoffs inference (TSKI) by exploiting the ideas of subsampling and e-values to address the difficulty caused by the serial dependence. We also generalize the robust knockoffs inference in Barber, Candès, and Samworth to the time series setting to relax the assumption of known covariate…

R^d 上空间数据的级数岭回归AI 解读

This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly generate irregularly spaced sampling sites, encompassing both pure increasing and mixed increasing domain frameworks. Specifically, we focus on a spatial trend regression model and a nonparametric regression model with spatially dependent…

随机分块协方差矩阵估计AI 解读

Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be divided into latent sub-populations with shared associative covariation within blocks and shared associative or dis-associative covariation across blocks. Unlike the block diagonal assumption, our block structure incorporates positive or…

高维比例渐近下全共形推断的训练条件覆盖性质AI 解读

We study the coverage properties of full conformal regression in the proportional asymptotic regime where the ratio of the dimension and the sample size converges to a constant. In this setting, existing theory tells us only that full conformal inference is unbiased, in the sense that its average coverage lies at the desired level when marginalized over both the new test point and the training data. Considerably less is known about the behaviour of these methods conditional…

稀疏投影后验的高维线性回归贝叶斯方法AI 解读

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to the sample size. We put a conjugate normal prior initially disregarding sparsity, but for making an inference, instead of the original multivariate normal posterior, we use the posterior distribution induced by a map transforming the vector…

超高维线性回归中的贝叶斯迭代筛选AI 解读

Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model probabilities. BITS can successfully integrate prior knowledge, if any, on effect sizes, and the number of true variables. BITS iteratively includes potential variables with the highest posterior probability accounting for the already selected…

用贝叶斯 VAR 预测宏观数据：稀疏还是稠密？取决于情境AI 解读

Vector autogressions (VARs) are widely applied when it comes to modeling and forecasting macroeconomic variables. In high dimensions, however, they are prone to overfitting. Bayesian methods, more concretely shrinkage priors, have shown to be successful in improving prediction performance. In the present paper, we introduce the semi-global framework, in which we replace the traditional global shrinkage parameter with group-specific shrinkage parameters. We show how this…

非线性动态的核估计AI 解读

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains scarce. This work studies a kernel-based estimation procedure for nonlinear dynamics within the reproducing kernel Hilbert space framework, focusing on nonlinear vector autoregressive models. We derive nonasymptotic probabilistic bounds…

高维广义尖峰Fisher矩阵中尖峰数量的检验推断AI 解读

The spiked Fisher matrix is a significant topic for two-sample problems in multivariate statistical inference. This paper is dedicated to testing the number of spikes in a high-dimensional generalized spiked Fisher matrix that relaxes the Gaussian population assumption and the diagonal constraints on the population covariance matrices. First, we propose a general test statistic predicated on partial linear spectral statistics to test the number of spikes, then establish the…

从快照数据学习密度演化AI 解读

Motivated by learning dynamical structures from static snapshot data, this paper presents a distribution-on-scalar regression approach for estimating the density evolution of a stochastic process from its noisy temporal point clouds. We propose an entropy-regularized nonparametric maximum likelihood estimator (E-NPMLE), which leverages the entropic optimal transport as a smoothing regularizer for the density flow. We show that the E-NPMLE has almost dimension-free…

凸与非凸惩罚似然的比较简论AI 解读

This paper compares convex and non-convex penalized likelihood methods in high-dimensional statistical modeling, focusing on their strengths and limitations. Convex penalties, like LASSO, offer computational efficiency and strong theoretical guarantees but often introduce bias in parameter estimation. Non-convex penalties, such as SCAD and MCP, reduce bias and achieve oracle properties but pose optimization challenges due to non-convexity. The paper highlights key…

排序与选择中的输入数据收集优化AI 解读

We study a ranking and selection (R&S) problem when all solutions share common parametric Bayesian input models updated with the data collected from multiple independent data-generating sources. Our objective is to identify the best system by designing a sequential sampling algorithm that collects input and simulation data given a budget. We adopt the most probable best (MPB) as the estimator of the optimum and show that its posterior probability of optimality converges to…

高维输入高斯过程模型的最优核学习AI 解读

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation involves too many input variables. For some simulation models, the outputs may only be significantly influenced by a small subset of the input variables, referred to as the ``active variables''. We propose an optimal kernel learning…

正则化零膨胀伯努利回归模型AI 解读

Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$ otherwise). One problem arising then is that, a proportion of the study subjects cannot experience the outcome of interest. This leads to an excessive presence of zeros in the study sample. This article is interested in estimating parameters…

基于基展开的协方差回归AI 解读

This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the regression-based covariance modeling framework and introduce a linear covariance selection model (LCSM) to encompass a broader spectrum of covariance structures when covariate information is available. Unlike existing methods, we do not…

用于时间序列预测的监督筛选与正则化因子方法AI 解读

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and Regularized Factor-based (SSRF) framework that systematically addresses high-dimensional predictor sets through a structured four-step procedure integrating both static and dynamic forecasting mechanisms. The static approach selects…

通过聚类估计多变量极值模型并选择阶数AI 解读

We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of clusters. The method consistently identifies the true order, i.e., the number of spectral atoms, and enjoys intuitive implementation in practice. Specifically, we introduce an extra penalty term to the well-known simplified average silhouette…

高维卷积秩回归的统计推断AI 解读

High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To solve this critical issue, high-dimensional convoluted rank regression has been recently proposed, introducing penalized convoluted rank regression estimators. However, these developed estimators cannot be directly used to make inference. In…