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植入分区模型下谱超图划分的一致性AI 解读

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph…

利用大型样本自协方差矩阵的奇异值识别因子数量AI 解读

Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on singular values of lagged sample auto-covariance matrices has been recently proposed in the literature with a reasonably good performance under some specific assumption on the strength of the factors. Inspired by this ratio estimator and as a first main contribution, this…

用 lava 恢复稠密与稀疏信号之和AI 解读

Common high-dimensional methods for prediction rely on having either a sparse signal model, a model in which most parameters are zero and there are a small number of nonzero parameters that are large in magnitude, or a dense signal model, a model with no large parameters and very many small nonzero parameters. We consider a generalization of these two basic models, termed here a “sparse $+$ dense” model, in which the signal is given by the sum of a sparse signal and a dense…

稀疏高维模型中假设检验与置信域的一般理论AI 解读

We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a novel decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high dimensional inference…

分层数据中的 lasso 回归建模AI 解读

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice, and propose an approach that bypasses this at almost no additional computational cost. Regarding model selection…

高维数据中的选择性因子提取AI 解读

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix.…

高维微观数据的合成控制框架：评估社区犯罪干预AI 解读

The synthetic control method is an increasingly popular tool for analysis of program efficacy. Here, it is applied to a neighborhood-specific crime intervention in Roanoke, VA, and several novel contributions are made to the synthetic control toolkit. We examine high-dimensional data at a granular level (the treated area has several cases, a large number of untreated comparison cases, and multiple outcome measures). Calibration is used to develop weights that exactly match…

遗传关联研究中检验 SNP 集合效应的广义 Higher CriticismAI 解读

It is of substantial interest to study the effects of genes, genetic pathways, and networks on the risk of complex diseases. These genetic constructs each contain multiple SNPs, which are often correlated and function jointly, and might be large in number. However, only a sparse subset of SNPs in a genetic construct is generally associated with the disease of interest. In this article, we propose the generalized higher criticism (GHC) to test for the association between an…

基于凹惩罚成对融合的亚组分析AI 解读

An important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup. This article considers the problem using samples drawn from a population consisting of subgroups with different mean values, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent…

协方差回归分析AI 解读

This article introduces covariance regression analysis for a p-dimensional response vector. The proposed method explores the regression relationship between the p-dimensional covariance matrix and auxiliary information. We study three types of estimators: maximum likelihood, ordinary least squares, and feasible generalized least squares estimators. Then, we demonstrate that these regression estimators are consistent and asymptotically normal. Furthermore, we obtain the high…

通过惩罚促进整合分析中的稀疏结构相似性AI 解读

For data with high-dimensional covariates but small sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single-dataset and several alternative multi-datasets methods. Under many scenarios, multiple datasets are expected to share common important covariates, that is, the corresponding models have similarity in their…

高维协方差矩阵的动态结构及其在投资组合配置中的应用AI 解读

Shaojun Guoa, John Leigh Boxb & Wenyang Zhangb*a Institute of Statistics and Big Data, Renmin University of China, Beijing, Chinab Department of Mathematics, University of York, York, United KingdomCONTACT Wenyang Zhang wenyang.zhang@york.ac.uk Department of Mathematics, The University of York, York YO10 5DD, United KingdomSupplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.ABSTRACTEstimation of high-dimensional covariance…

用于高维估计的非局部先验AI 解读

Jointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Nonlocal priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size n increases, while nonspurious parameter estimates are not shrunk.…

检测高维协方差矩阵微弱与稀疏差异的加权统计量AI 解读

This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function…

用于估计个体化治疗规则的残差加权学习AI 解读

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has…

用因子 Copula 建模高维依赖结构AI 解读

This article presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high-dimensional applications, involving 50 or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied…

无对称性与轻尾假设下的高维均值回归估计AI 解读

Summary Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently…

高维两样本检验AI 解读

Summary We propose new methodology for two-sample testing in high dimensional models. The methodology provides a high dimensional analogue to the classical likelihood ratio test and is applicable to essentially any model class where sparse estimation is feasible. Sparse structure is used in the construction of the test statistic. In the general case, testing then involves non-nested model comparison, and we provide asymptotic results for the high dimensional setting. We put…

高维概率主成分分析中的噪声方差估计AI 解读

Summary We develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons for an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator by…

大型已实现协方差矩阵的建模、预测与投资组合选择AI 解读

Summary We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso‐type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics as…

用自适应稀疏网格求解高维动态模型AI 解读

We present a exible and scalable method for computing global solutions of high-dimensional stochastic dynamic models. Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm. With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids. Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance in regions…

单调性约束下的非参数工具变量估计AI 解读

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance.In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators.We assume that the regression function is monotone and consider sieve estimators that enforce the monotonicity constraint.We define a restricted measure of…

高维数据下的项目评估与因果推断AI 解读

The accepted manuscript version (last revised 5 Jan 2018 (v8)) has 118 pages, 3 tables, 11 figures, and includes supplementary appendix. This version corrects some typos in Example 2 of the published version. This supplement contains 11 appendices with additional results and some omitted proofs. Appendices F-J include additional results for Sections 2-7, respectively. Appendix K gathers auxiliary results on algebra of covering entropies. Appendices L and M contain the proofs…

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