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通过SLIDE实现具有全局最优性的Ising模型重建AI 解读

The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction process, but finding the underlying Ising model from the least amount of observed samples in a computationally efficient manner has been historically challenging for half a century. Using sparsity learning, we present an approach named SLIDE…

PALAR：用相对丰度预测变量估计绝对丰度回归效应AI 解读

High-dimensional compositional data are ubiquitous in omics research. Microbiome sequencing experiments measure the relative abundances (proportions) of microbial features, while the absolute abundances within the ecosystem remain unobserved. Most regression methods with microbial relative abundance predictors rely on log-ratio transformations and typically impose sparsity on the regression coefficients to manage high dimensionality. However, we show that the sparsity…

基于 Grothendieck 散度的函数型数据极小极大两样本检验AI 解读

Our proposed approach addresses the challenges associated with nonparametric two-sample testing for densely measured functional data. These challenges stem from the high dimensionality of data and the nature of the observation scheme. We introduce a novel metric concept for random functions known as Grothendieck’s divergence to overcome these challenges, which satisfies the homogeneity-zero equivalence property. Our approach uses a pre-smoothing technique on densely measured…

聚合投影法：组因子模型的新方法AI 解读

Identifying the global factors among grouped data is crucial in the group factor model. In this paper, we propose a novel objective function for the task by maximizing the average of correlations between the latent global factors and group factors, solved through the eigen-decomposition of the aggregated projection matrix. Our method is not only computationally efficient but also robust to strongly correlated local factors. We establish the consistency of the global/local…

度量空间上张量积再生核希尔伯特空间的方差分析AI 解读

Many methods have been developed to analyze complex data, such as non-Euclidean shape, network, and manifold data. However, there is a lack of methods for studying interactions among complex data. In this article, we first propose a novel kernel function for a metric space and construct its associated reproducing kernel Hilbert space. The new nonstationary kernel function provides a flexible and powerful tool for learning complex structures in non-Euclidean data. We then…

学生化独立性检验：随机提升方法AI 解读

The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various strengths and limitations. One problem is that their test statistics tend to converge to asymptotic null distributions involving second-order Wiener chaos, which are hard to compute and need approximation or permutation techniques that use…

Green 匹配：复杂动力系统参数估计的高效方法AI 解读

Abstract Parameters of differential equations are essential to characterize intrinsic behaviours of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for complex systems with general-order differential operators, such as motion dynamics. This article presents Green’s matching, a computationally tractable and statistically efficient two-step method, which only needs to approximate…

层间依赖多层网络的一致社群检测AI 解读

Community detection in multi-layer networks, which aims at finding groups of nodes with similar connective patterns among all layers, has attracted tremendous interests in multi-layer network analysis. Most existing methods are extended from those for single-layer networks, which assume that different layers are independent. In this article, we propose a novel community detection method in multi-layer networks with inter-layer dependence, which integrates the stochastic…

通过度量空间中的度量分布函数开展非参数统计推断AI 解读

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the…

通过随机积分检验高维两样本均值相等AI 解读

Testing the equality of the means in two samples is a fundamental statistical inferential problem. Most of the existing methods are based on the sum-of-squares or supremum statistics. They are possibly powerful in some situations, but not in others, and they do not work in a unified way. Using random integration of the difference, we develop a framework that includes and extends many existing methods, especially in high-dimensional settings, without restricting the same…

具有持仓数量约束的高维投资组合选择AI 解读

The expanding number of assets offers more opportunities for investors but poses new challenges for modern portfolio management (PM). As a central plank of PM, portfolio selection by expected utility maximization (EUM) faces uncontrollable estimation and optimization errors in ultrahigh-dimensional scenarios. Past strategies for high-dimensional PM mainly concern only large-cap companies and select many stocks, making PM impractical. We propose a…

球协方差：Banach 空间中的通用依赖度量AI 解读

Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g, different brain subcortical structures) often reside in some Banach spaces, and hence their relationship cannot be well characterized by most of the existing measures of dependence such as correlation coefficients developed in Hilbert spaces. To…

一种通用的确定独立筛选程序AI 解读

Wenliang Pana, Xueqin Wanga, Weinan Xiaoa & Hongtu Zhub*a Department of Statistical Science, School of Mathematics, Sun Yat-Sen University, Guangzhou, P. R. Chinab Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TXCONTACT Hongtu Zhu hzhu5@mdanderson.org Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX 77030Supplementary materials for this article are available online. Please go to…

球散度：非参数两样本检验AI 解读

In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in separable Banach spaces, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. It is therefore robust to…

Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations, and are incapable of characterizing non-linear conditional relationship including non-monotonic relationship. To overcome this limitation, we introduces a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure…

基于指数平方损失的稳健变量选择AI 解读

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this…

基于广义Kendall’s Tau的多性状关联检验AI 解读

In many genetics studies, especially in the investigation of mental illness and behavioral disorders, it is common for researchers to collect multiple phenotypes to characterize the complex disease of interest. It may be advantageous to analyze those phenotypic measurements simultaneously if they share a similar genetic mechanism. In this study, we present a nonparametric approach to studying multiple traits together rather than examining each trait separately. Through…