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高维线性模型中线性泛函的估计：从稀疏到非稀疏AI 解读

can be sparse or non-sparse and predictors can be strongly or weakly correlated. The proposed method is simple for implementation. Numerical and theoretical results demonstrate the competitive advantages of the proposed method for a wide range of problems.

稠密因子增强模型下的岭回归AI 解读

This article establishes a comprehensive theory of the optimality, robustness, and cross-validation selection consistency for the ridge regression under factor-augmented models with possibly dense idiosyncratic information.Using spectral analysis for random matrices, we show that the ridge regression is asymptotically efficient in capturing both factor and idiosyncratic information by minimizing the limiting predictive loss among the entire class of spectral regularized…

利用机器学习推断处理特定生存曲线AI 解读

In the absence of data from a randomized trial, researchers may aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves, that is, the survival curves were the population under study to be assigned to receive the treatment or not. Under certain conditions, including that all confounders of the treatment-outcome relationship are observed,…

高维稀疏卷积秩回归AI 解读

Wang et al. studied the high-dimensional sparse penalized rank regression and established its nice theoretical properties. Compared with the least squares, rank regression can have a substantial gain in estimation efficiency while maintaining a minimal relative efficiency of 86.4%. However, the computation of penalized rank regression can be very challenging for high-dimensional data, due to the highly nonsmooth rank regression loss. In this work we view the rank regression…

多模态影像数据复杂依赖结构的统计推断AI 解读

Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multitask fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing…

高维在线变点检测中的统计推断AI 解读

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a…

高维稀疏协方差函数估计的自适应函数阈值法AI 解读

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications.In this article, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n.Aided by the Hilbert-Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of…

通过退火分布流高效进行多峰抽样AI 解读

Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this difficulty by fitting an invertible transformation mapping, called a transport map, between a reference probability measure and the target distribution, so that sampling from the target distribution can be achieved by pushing forward a reference…

高维非高斯空间场的可扩展贝叶斯输运映射AI 解读

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution.We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes.This enables regularization and uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map.We then focus on inferring the distribution of a nonstationary spatial field…

基于条件秩效用的大数据分类特征筛选AI 解读

Feature screening is a commonly used strategy to eliminate irrelevant features in high-dimensional classification. When one encounters big datasets with both high dimensionality and huge sample size, the conventional screening methods become computationally costly or even infeasible. In this article, we introduce a novel screening utility, Conditional Rank Utility (CRU), and propose a distributed feature screening procedure for the big-data classification. The proposed CRU…

高维阈值参数的显著性检验：个体化最小临床重要差异应用AI 解读

This work is motivated by learning the individualized minimal clinically important difference, a vital concept to assess clinical importance in various biomedical studies. We formulate the scientific question into a high-dimensional statistical problem where the parameter of interest lies in an individualized linear threshold. The goal is to develop a hypothesis testing procedure for the significance of a single element in this parameter as well as of a linear combination of…

度异质性社会网络中高维节点属性的变量选择AI 解读

We consider a class of network models, in which the connection probability depends on ultrahigh-dimensional nodal covariates (homophily) and node-specific popularity (degree heterogeneity). A Bayesian method is proposed to select nodal features in both dense and sparse networks under a mild assumption on popularity parameters. The proposed approach is implemented via Gibbs sampling. To alleviate the computational burden for large sparse networks, we further develop a working…

知识迁移下高维广义线性模型的估计与推断AI 解读

Transfer learning provides a powerful tool for incorporating data from related studies into a target study of interest. In epidemiology and medical studies, the classification of a target disease could borrow information across other related diseases and populations. In this work, we consider transfer learning for high-dimensional generalized linear models (GLMs). A novel algorithm, TransHDGLM, that integrates data from the target study and the source studies is proposed.…

用于高维时间序列聚类的因子建模AI 解读

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure.Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact on all the time series concerned.Our setting also offers the flexibility that some time series may not belong to any clusters.The consistency with explicit convergence rates is established for the estimation of the common factors, the…

利用枢纽模型及其变体推断隐含网络AI 解读

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is…

存在混杂时的非线性因果发现AI 解读

This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption. Then, we propose a novel method, named the Deconfounded Functional Structure Estimation (DeFuSE), consisting of a deconfounding adjustment to remove the confounding effects and a sequential procedure to estimate the causal order of…

结合共形预测与加权秩和的两样本条件分布检验AI 解读

We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and statistical inference scenarios, including transfer learning and causal predictive inference. We develop a nonparametric test procedure inspired from the conformal prediction framework. The construction of our test statistic combines recent…

高维函数型数据的最优线性判别分析AI 解读

Most of existing methods of functional data classification deal with one or a few processes. In this work we tackle classification of high-dimensional functional data, in which each observation is potentially associated with a large number of functional processes, p, which is comparable to or even much larger than the sample size n. The challenge arises from the complex inter-correlation structures among multiple functional processes, instead of a diagonal correlation for a…

骨架聚类：维度无关的密度辅助聚类AI 解读

We introduce a density-aided clustering method called Skeleton Clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density measures that are less dependent on the dimension but have intuitive geometric interpretations. The clustering framework constructs a concise representation of the given data as an intermediate step and can be thought of as a combination of…

不规则位置与跨位置非平稳下的半参数动态函数系数时空自回归模型AI 解读

Nonlinear dynamic modeling of spatio-temporal data is often a challenge, especially due to irregularly observed locations and location-wide nonstationarity.In this article we propose a semiparametric family of Dynamic Functional-coefficient Autoregressive Spatio-Temporal (DyFAST) models to address the difficulties.We specify the autoregressive smoothing coefficients depending dynamically on both a concerned regime and location so that the models can characterize not only the…

高阶最小二乘：评估线性因果模型的局部拟合优度AI 解读

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of…

潜在因子回归与稀疏回归是否充分？AI 解读

We propose the Factor Augmented sparse linear Regression Model (FARM) that not only encompasses both the latent factor regression and sparse linear regression as special cases but also bridges dimension reduction and sparse regression together. We provide theoretical guarantees for the estimation of our model under the existence of sub-Gaussian and heavy-tailed noises (with bounded (1+x)-th moment, for all x>0), respectively. In addition, the existing works on supervised…

高维单指标模型假设检验的随机投影方法AI 解读

In this article, we consider the problem of hypothesis testing in high-dimensional single-index models. First, we study the feasibility of applying the classical F-test to a single-index model when the dimension of covariate vector and sample size are of the same order, and derive its asymptotic null distribution and asymptotic local power function. For the ultrahigh-dimensional single-index model, we construct F-statistics based on lower-dimensional random projections of…

具有高维协变量的多臂老虎机自适应算法AI 解读

This article studies an important sequential decision making problem known as the multi-armed stochastic bandit problem with covariates. Under a linear bandit framework with high-dimensional covariates, we propose a general multi-stage arm allocation algorithm that integrates both arm elimination and randomized assignment strategies. By employing a class of high-dimensional regression methods for coefficient estimation, the proposed algorithm is shown to have near optimal…