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凸惩罚高维回归的根本障碍AI 解读

In high-dimensional regression, we attempt to estimate a parameter vector β0∈Rp from n≲p observations {(yi,xi)}i≤n, where xi∈Rp is a vector of predictors and yi is a response variable. A well-established approach uses convex regularizers to promote specific structures (e.g., sparsity) of the estimate βˆ while allowing for practical algorithms. Theoretical analysis implies that convex penalization schemes have nearly optimal estimation properties in certain settings. However,…

稀疏贝叶斯预测密度估计的极小极大最优性AI 解读

We study predictive density estimation under Kullback–Leibler loss in ℓ0-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r

异方差主成分分析：算法、最优性与应用AI 解读

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis…

基于重复测量的反卷积估计量的一致收敛AI 解读

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the…

高维张量时间序列的因子模型AI 解读

Large tensor (multi-dimensional array) data routinely appear nowadays in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this article we present a factor model approach to the analysis of high-dimensional dynamic tensor time series and multi-category dynamic transport networks. This article presents two estimation procedures along with their theoretical properties and…

采用可逆 SGLD 提议的小批量 Metropolis–Hastings 方法AI 解读

Traditional Markov chain Monte Carlo (MCMC) algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis–Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm…

超高维协方差矩阵序列中的变化点估计AI 解读

This article considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step, we use the components after…

两个时空随机场空间特征局部差异的检测AI 解读

Comparing the spatial characteristics of spatiotemporal random fields is often at demand. However, the comparison can be challenging due to the high-dimensional feature and dependency in the data. We develop a new multiple testing approach to detect local differences in the spatial characteristics of two spatiotemporal random fields by taking the spatial information into account. Our method adopts a two-component mixture model for location wise p-values and then derives a…

嵌入学习AI 解读

Numerical embedding has become one standard technique for processing and analyzing unstructured data that cannot be expressed in a predefined fashion. It stores the main characteristics of data by mapping it onto a numerical vector. An embedding is often unsupervised and constructed by transfer learning from large-scale unannotated data. Given an embedding, a downstream learning method, referred to as a two-stage method, is applicable to unstructured data. In this article,…

数据重编码中协变量与结果的正则化最优传输AI 解读

When databases are constructed from heterogeneous sources, it is not unusual that different encodings are used for the same outcome. In such case, it is necessary to recode the outcome variable before merging two databases. The method proposed for the recoding is an application of optimal transportation where we search for a bijective mapping between the distributions of such variable in two databases. In this article, we build upon the work by Garés et al., where they…

高维非平稳 VAR 模型的结构断点检测与参数联合估计AI 解读

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and…

高维相关数据中未观测协变量的估计与调整AI 解读

Many high dimensional and high-throughput biological datasets have complex sample correlation structures, which include longitudinal and multiple tissue data, as well as data with multiple treatment conditions or related individuals. These data, as well as nearly all high-throughput 'omic' data, are influenced by technical and biological factors unknown to the researcher, which, if unaccounted for, can severely obfuscate estimation of and inference on the effects of…

平滑样条半参数密度模型AI 解读

Jiahui Yua, Jian Shib, Anna Liuc & Yuedong Wangd*a Department of Mathematics and Statistics, Boston University, Boston, MAb PayPal, San Jose, CAc Department of Mathematics and Statistics, University of Massachusetts, Amherst, MAd Department Statistics and Applied Probability, University of California, Santa Barbara, CAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are…

高维中介假设的多重检验程序AI 解读

Mediation analysis is of rising interest in epidemiology and clinical trials. Among existing methods, the joint significance (JS) test yields an overly conservative type I error rate and low power, particularly for high-dimensional mediation hypotheses. In this article we develop a multiple-testing procedure that accurately controls the family-wise error rate (FWER) and the false discovery rate (FDR) when testing high-dimensional mediation hypotheses. The core of our…

分组回归与稀疏广义加性模型的尖峰—厚尾组 LassoAI 解读

–We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the first nonparametric variant of the spike-and-slab lasso methodology. Our model simultaneously performs group selection and estimation, while our fully Bayes treatment of the mixture proportion allows for model complexity control and…

半参数因子模型中的同质性与结构识别AI 解读

Factor modeling is an essential tool for exploring intrinsic dependence structures in financial and economic studies through the construction of common latent variables, including the famous Fama–French three factor models for the description of asset returns in finance. However, most of the existing statistical methods for analyzing latent factors have been developed through a linear approach. In this article, we consider a semiparametric factor model and present a…

依赖过程条件独立检验的投影方法AI 解读

Conditional independence is a fundamental concept in many scientific fields. In this article, we propose a projective approach to measuring and testing departure from conditional independence for dependent processes. Through projecting high-dimensional dependent processes on to low-dimensional subspaces, our proposed projective approach is insensitive to the dimensions of the processes. We show that, under the common β-mixing conditions, our proposed projective test…

局部平稳时间序列的预测AI 解读

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in nonstationary time series. In contrast to the currently available methods for this problem the predictor developed here does not rely on fitting an autoregressive model and does not require a vanishing trend. The finite sample properties of the new methodology are illustrated by means of a…

因子数增长时充分预测的非参数估计与共形推断AI 解读

The sufficient forecasting (SF) provides a nonparametric procedure to estimate forecasting indices from high-dimensional predictors to forecast a single time series, allowing for the possibly nonlinear forecasting function. This article studies the asymptotic theory of the SF with a diverging number of factors and develops its predictive inference. First, we revisit the SF and explore its connections to Fama–MacBeth regression and partial least squares. Second, with a…

高维数据下条件平均处理效应的估计AI 解读

Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the…

无矩约束的高维因子分析AI 解读

Large-dimensional factor model has drawn much attention in the big-data era, to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model typically requires finite fourth moment of the data, which ignores the effect of heavy-tailedness and thus may result in unrobust or even inconsistent estimation of the factor space and common components. In this article, we propose to recover the…

高维因子随机波动模型中的杠杆效应、非对称性与厚尾AI 解读

We develop a factor stochastic volatility model that incorporates leverage effects, return asymmetry, and heavy tails across all systematic and idiosyncratic model components. Our model leads to a flexible high-dimensional dependence structure that allows for time-varying correlations, tail dependence, and volatility response to both systematic and idiosyncratic return shocks. We develop an efficient Markov chain Monte Carlo algorithm for posterior estimation based on the…

具有同质结构的高维动态协方差矩阵AI 解读

High-dimensional covariance matrices appear in many disciplines. Much literature has devoted to the research in high-dimensional constant covariance matrices. However, constant covariance matrices are not sufficient in applications, for example, in portfolio allocation, dynamic covariance matrices would be more appropriate. As argued in this article, there are two difficulties in the introduction of dynamic structures into covariance matrices: (1) simply assuming each entry…

巴西失业与失业保险对犯罪的影响AI 解读

We investigate the impact of job loss on crime and the mitigating role of unemployment benefits, exploiting detailed individual‐level data linking employment careers, criminal records, and welfare registries for the universe of male workers in Brazil. The probability of committing crimes increases on average by 23% for workers displaced by mass layoffs, and by slightly less for their cohabiting sons. Using causal forests, we show that the effect is entirely driven by young…