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利用统计推断增强 AI 生成生物医学图像的可信度AI 解读

Generative artificial intelligence (AI) has transformed the biomedical imaging field through image synthesis, addressing challenges of data availability, privacy, and diversity in biomedical research. This paper proposes a novel nonparametric method within the functional data framework to discern significant differences between the mean and covariance functions of original and synthetic biomedical imaging data, thereby enhancing the fidelity and utility of synthetic data.…

通过特征值分析识别高维时间序列结构AI 解读

Cross-sectional structures and temporal tendency are important features of high-dimensional time series. Based on eigen-analysis on sample covariance matrices, we propose a novel approach to identifying four popular structures of high-dimensional time series, which are grouped in terms of factor structures and stationarity. The proposed three-step method includes a ratio statistic of empirical eigenvalues;a projected Augmented Dickey-Fuller Test;a new unit-root test based on…

维度递增随机图模型中的似然比检验AI 解读

We explore the Wilks phenomena in two random graph models: the β-model and the Bradley–Terry model. For two increasing dimensional null hypotheses, including a specified null H0:βi=βi0 for i=1,…,r and a homogenous null H0:β1=⋯=βr, we reveal high dimensional Wilks’ phenomena that the normalized log-likelihood ratio statistic, [2{l(β̂)−l(β̂0)}−r]/(2r)1/2, converges in distribution to the standard normal distribution as r goes to infinity. Here, l(β) is the log-likelihood…

ℓ∞ 扰动下对抗训练估计量的渐近行为AI 解读

Adversarial training has been proposed to protect machine learning models against adversarial attacks. This paper focuses on adversarial training under 𝓁∞-perturbation, which has recently attracted much research attention. The asymptotic behavior of the adversarial training estimator is investigated in the generalized linear model. The results imply that the asymptotic distribution of the adversarial training estimator under 𝓁∞-perturbation could put a positive probability…

稀疏贝叶斯多维项目反应理论AI 解读

Multivariate Item Response Theory (MIRT) is sought-after widely by applied researchers looking for interpretable (sparse) explanations underlying response patterns in questionnaire data. There is, however, an unmet demand for such sparsity discovery tools in practice. Our article develops a Bayesian platform for binary and ordinal item MIRT which requires minimal tuning and scales well on large datasets due to its parallelizable features. Bayesian methodology for MIRT models…

具有预言性质与几何收敛性的通信高效分布式稀疏学习AI 解读

This article introduces two highly efficient distributed non-convex sparse learning algorithms. Our approach accommodates non-convexity in both the loss function and penalty, acknowledging the potential non-uniqueness of local minimizers due to the inherent non-convexity. The development of an algorithm that ensures convergence to a locally minimal solution with desired statistical properties becomes imperative in this context. To overcome this challenge, we propose a…

利用低秩结构进行多维领域泛化AI 解读

In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make…

网络变系数模型AI 解读

We propose a novel network-varying coefficient model that extends traditional varying coefficient models to accommodate network data. The main idea is to model the regression coefficients as the functions of the latent “locations” of network nodes that drive formation of the network. To estimate the model, we identify the latent “locations” via the latent space model and then develop an iterative projected gradient descent algorithm by optimizing the network parameters and…

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…

高维离散数据的程度异质性潜在类别分析AI 解读

The latent class model is a widely used mixture model for multivariate discrete data. Besides the existence of qualitatively heterogeneous latent classes, real data often exhibit additional quantitative heterogeneity nested within each latent class. The modern latent class analysis also faces extra challenges, including the high-dimensionality, sparsity, and heteroscedastic noise inherent in discrete data. Motivated by these phenomena, we introduce the Degree-heterogeneous…

重复测量数据的深度回归AI 解读

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected deep neural network (DNN) estimators with flexible shapes. A novel theoretical framework allowing arbitrary sampling frequency is established by adopting empirical process techniques to tackle clustered dependence. We then consider the DNN…

高维线性假设检验的一种新方法AI 解读

This paper proposes an innovative double power-enhanced testing procedure for inference on high-dimensional linear hypotheses in high-dimensional regression models. Through a projection approach that aims to separate useful inferential information from the nuisance one, our proposed test accurately accounts for the impact of high-dimensional nuisance parameters. We discover that with a carefully-designed projection matrix, the projection procedure enables us to transform the…

大型向量自回归模型中的网络格兰杰因果关系发现AI 解读

This article proposes novel inferential procedures for discovering the network Granger causality in highdimensional vector autoregressive models.In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR).The first procedure is based on the limiting normal distribution of the t-statistics with the debiased lasso estimator.The second procedure is its bootstrap version.We also provide a robustification of the first…

高维椭圆模型中 R² 统计量的自适应调整AI 解读

The 𝑅2 statistic and its classic adjusted version, say 𝑅*2, tend to overestimate the multiple correlation coefficient when dealing with multivariate data that exhibit heavy tails and tail dependence. This can result in an incorrect significance of correlation in high-dimensional scenarios. A new adaptive adjustment to the 𝑅2 statistic is proposed in this paper, which applies to a general population model that covers the family of elliptical distributions and an…

利用高维部分线性半参数混合效应模型比较纵向轨迹AI 解读

In longitudinal research, it is essential to compare sets of trajectories, commonly seen as changes over time in different treatment or patient groups. This paper presents a partial linear semiparametric mixed-effects model (PLSMM) for the analysis and comparison of nonlinear longitudinal trajectories with high-dimensional covariates across groups. Our flexible modeling framework can effectively handle complex temporal effects and extensive data while providing statistical…

再生核希尔伯特空间上的非参数期望短缺回归估计与推断AI 解读

Expected shortfall (ES) has emerged as an important metric for characterizing the tail behavior of a random outcome, specifically associated with rarer events that entail severe consequences. In climate science, the threats of flooding and heatwaves loom large, impacting natural environments and human communities. In actuarial studies, a key observation in modeling insurance claim sizes is that features exhibit distinct effects in explaining small and large claims. This…

含随机变点的区间删失失效时间数据估计与变量选择AI 解读

Motivated by a breast cancer study, we consider regression analysis of interval-censored failure time data in the presence of a random change point. Although a great deal of literature on interval-censored data has been established, there does not seem to exist an established method that can allow for the existence of random change points. Such data can occur in, for example, clinical trials where the risk of a disease may dramatically change when some biological indexes of…

利用广义变系数模型检测不规则区域中的局部信号AI 解读

In spatial analysis, it is essential to understand and quantify spatial or temporal heterogeneity. This paper focuses on the generalized spatially varying coefficient model (GSVCM), a powerful framework to accommodate spatial heterogeneity by allowing regression coefficients to vary in a given spatial domain. We propose a penalized bivariate spline method for detecting local signals in GSVCM. The key idea is to use bivariate splines defined on triangulation to approximate…

超高维协方差矩阵的两样本检验AI 解读

In this article, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples.Our proposed methodology relies on a data splitting procedure and a comparison of a set of well selected eigenvalues of the sample covariance matrices on the split datasets.Compared to the existing methods, our methodology is adaptive in the sense that (i). it…

多元函数型线性回归中的系数形状对齐AI 解读

In multivariate functional data analysis, different functional covariates often exhibit homogeneity. The covariates with pronounced homogeneity can be analyzed jointly within the same group, offering a parsimonious approach to modeling multivariate functional data. In this article, a novel grouped multiple functional regression model with a new regularization approach termed “coefficient shape alignment” is developed to tackle functional covariates homogeneity. The modeling…

高维函数型时间序列的建模与预测AI 解读

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from…

贝叶斯动态矩阵因子模型AI 解读

The growth in data volume and the expansion in data dimensionality are challenging the analysis of high-dimensional matrix time series. Factor models for matrix-valued high-dimensional time series are a powerful tool for reducing the dimensionality of the variables with low-rank structures. However, existing high-dimensional matrix factor models are nearly all static and struggle to capture the dynamics and time evolution of data. In this article, a dynamic matrix factor…

调节效应的因果机器学习AI 解读

It is valuable for any decision maker to know the impact of decisions (treatments) on average and for subgroups.The causal machine learning literature has recently provided tools for estimating group average treatment effects (GATE) to better describe treatment heterogeneity.This article addresses the challenge of interpreting such differences in treatment effects between groups while accounting for variations in other covariates.We propose a new parameter, the balanced…

因子网络自回归AI 解读

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents (“multilayer network”), which are summarized into a smaller number of network matrices (“network factors”) through a novel tensor-based principal component approach. We provide consistency and asymptotic normality results for the estimation of the factors, their loadings, and…