Multivariate Medial Correlation with applications

Estimating a graphical intra-class correlation coefficient (GICC) using multivariate probit-linear mixed models

Data reproducibility is a critical issue in all scientific experiments. In this manuscript, we consider the problem of quantifying the reproducibility of graphical measurements. We generalize the concept of image intra-class correlation coefficient (I2C2) and propose the concept of the graphical intra-class correlation coefficient (GICC) for such purpose. The concept of GICC is based on multivariate probit-linear mixed effect models. We will present a Markov Chain EM (MCEM) algorithm for estimating the GICC. Simulations results with varied settings are demonstrated and our method is applied to…

高斯过程的偏相关网络

Partial correlation networks of Gaussian processes

本文提出高斯过程中偏相关网络的新型表征，通过构建谱内-外过程类，揭示了多变量高斯过程的条件独立性条件，并展示了现有方法的局限性。

多元数据的联合均值与相关性回归模型

Joint Mean and Correlation Regression Models for Multivariate Data

本文提出一种联合均值与相关性回归模型，可同时回归多元响应的均值与相关性，并开发了联合估计方程和迭代估计程序，模拟验证了其有限样本性能，应用于苏格兰38种步甲虫数据，揭示了环境协变量对物种丰度的影响及体长对物种间相关性的驱动作用。

基于多元秩距离相关的无分布、无模型多元特征筛选

Distribution-free and Model-free Multivariate Feature Screening via Multivariate Rank Distance Correlation

针对现有特征筛选方法依赖分布/模型假设、多适配单变量响应的问题，提出基于多元秩距离相关的MrDc-SIS方法，具备多项优良特性，经理论证明与模拟验证性能更优，可应用于多组学癌症数据筛选。

Multivariate Functional Additive Mixed Models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the resp…

Bayesian analysis of multivariate stochastic volatility with skew distribution

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian prior works allow this approach to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Analyses of daily stock returns are illustrated. Empirical results show that the time-varying correlations and the sparse skew structure contribute to im…

Modelling Correlation Matrices in Multivariate Dyadic Data: Latent Variable Models for Intergenerational Exchanges of Family Support

We define a model for the joint distribution of multiple continuous latent variables which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between generations and complementarity of different kinds of help. We propose an MCMC procedure for estimating the model which maintains the positive definiteness of the implied correlation matrices, and describe theoretical results wh…

Correlation between Multivariate Datasets, from Inter-Graph Distance computed using Graphical Models Learnt With Uncertainties

We present a method for simultaneous Bayesian learning of the correlation matrix and graphical model of a multivariate dataset, along with uncertainties in each, to subsequently compute distance between the learnt graphical models of a pair of datasets, using a new metric that approximates an uncertainty-normalised Hellinger distance between the posterior probabilities of the graphical models given the respective dataset; correlation between the pair of datasets is then computed as a corresponding affinity measure. We achieve a closed-form likelihood of the between-columns correlation matrix b…

基于因果和局部相关性的多元时间序列分类网络

Causal and Local Correlations Based Network for Multivariate Time Series Classification

针对现有多元时间序列分类方法忽略维度空间相关性与特征局部相关性的问题，本研究提出CaLoNet，通过因果建模维度成对空间相关性得图结构、关系提取网络融合局部相关性得长期依赖特征并整合入图神经网络，在UEA数据集上取得与最优方法相当的性能。

具有多元混合分布的一阶多元整数值自回归模型

First-order multivariate integer-valued autoregressive model with multivariate mixture distributions

本文提出一阶多元整数值自回归模型以灵活刻画多元整数值时间序列的相关结构，建立平稳性与遍历性，并基于EM算法进行参数估计，通过模拟和真实犯罪数据验证了模型优势。

多变量极值中部分尾相关性的假设检验

Hypothesis testing for partial tail correlation in multivariate extremes

本文提出了一种用于多变量极值中部分尾相关性检验的方法，通过尾部回归和极值协方差矩阵分析，揭示极值依赖结构中的稀疏性。

多变量纵向研究中的一种时间变化和协变量依赖的相关模型

A Time-Varying and Covariate-Dependent Correlation Model for Multivariate Longitudinal Studies

本文提出TiVAC模型，用于多变量纵向研究中时间变化和协变量依赖的相关性建模，通过模拟和案例研究验证其在不同设置下的优越性。

A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series

A novel approach for dynamic modeling and forecasting of realized covariance matrices is proposed. Realized variances and realized correlation matrices are jointly estimated. The one-to-one relationship between a positive definite correlation matrix and its associated set of partial correlations corresponding to any vine specification is used for data transformation. The model components therefore are realized variances as well as realized standard and partial correlations corresponding to a daily log-return series. As such, they have a clear practical interpretation. A method to select a regu…

基于距离的Chatterjee相关：一种新的广义稳健的有向关联度量，适用于多元实值和复值数据

Distance-based Chatterjee correlation: a new generalized robust measure of directed association for multivariate real and complex-valued data

本研究提出基于距离的Chatterjee相关，一种稳健的非参数度量，用于多元实值和复值数据的有向关联，支持因果方向推断。

Second order semi-parametric inference for multivariate log Gaussian Cox processes

This paper introduces a new approach to inferring the second order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model we exploit the availability of several types of points to construct a second-order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the inten…

Assessing phenotypic correlation through the multivariate phylogenetic latent liability model

Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the correlation between multiple types of data, while simultaneously controlling for their unknown shared evolutionary history informed through molecular sequences. The latent formulation enables us to consider in a single model combinations of continuous traits, discrete binary traits and discrete traits with multiple ordered and unordered states. Previous approache…

二分类数据中相关性与Cohen's Kappa的线性关系及模拟具有指定Kappa矩阵的多变量名义和有序数据

A Linear Relationship between Correlation and Cohen's Kappa for Binary Data and Simulating Multivariate Nominal and Ordinal Data with Specified Kappa Matrix

本文发现了二分类数据中相关性与Cohen's Kappa的线性关系，提出了计算Kappa精确下限的算法，并基于边际数据重排与求解线性方程组，实现生成具有指定Kappa矩阵的多变量名义和有序数据。

基于配对卦限的新多元非参数关联度量

A new multivariate and non-parametric association measure based on paired orthants

本文提出一种基于配对卦限概念的多变量非参数关联度量方法，不仅能评估多变量间的相互关联性，还能确定变量的特定倾向。

在多变量空间模型中引入相关块金效应：在Argo海洋数据中的应用

Incorporating Correlated Nugget Effects in Multivariate Spatial Models: An Application to Argo Ocean Data

本文提出带相关块金效应的高斯与非高斯分层多变量Matérn-SPDE模型，用于Argo海洋温盐数据，证明该模型能提高参数估计和空间预测精度，并揭示传统独立噪声假设可能高估场间相关性。

Multivariate Generalised Linear Mixed Models With Graphical Latent Covariance Structure

This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that each of the several responses studied is modelled using a generalised linear mixed models (GLMM) containing random components representing the clusters. We construct a MGLMM by assuming that the distribution of each of the random components representing the clusters is the marginal distribution of a (sufficiently regular) multivariate elliptically contoured dis…

Bayesian inference for general Gaussian graphical models with application to multivariate lattice data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcom…

Multivariate Generalized Linear Mixed Models for Count Data

Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate set of responses, measuring the correlation between them through random effects that follows a multivariate normal distribution. This model is based on a GLMM with a random intercept and the estimation process remains the same as a standard GLMM with random effects integrated out via Laplace approximation. We efficiently implemented this model through the TM…

Multivariate stochastic volatility using state space models

A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the convolution between the Wishart and the multivariate singular beta distribution. A multiplicative model based on the generalized inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility and a flexible sequential volatility upd…

一种用于可解释相关矩阵模型的图框架

A graphical framework for interpretable correlation matrix models

本文提出一种构建具有用户自定义图结构相关矩阵模型的新方法，结合 Penalized Complexity 框架定义先验，避免参数二次增长并提升可解释性，通过多元回归、疾病制图和纵向联合建模三个应用验证了方法的有效性。

Spatially Penalised Registration of Multivariate Functional Data

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase r…

Separable covariance arrays via the Tucker product, with applications to multivariate relational data

Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as well as correlation among the variables. A possible model for matrix-valued data is the class of matrix normal distributions, which is parametrized by two covariance matrices, one for each index set of the data. In this article we describe an extension of the matrix normal model to accommodate multidimensional data arrays, or tensors. We generate a class of…

Nonstationary Multivariate Gaussian Processes for Electronic Health Records

We propose multivariate nonstationary Gaussian processes for jointly modeling multiple clinical variables, where the key parameters, length-scales, standard deviations and the correlations between the observed output, are all time dependent. We perform posterior inference via Hamiltonian Monte Carlo (HMC). We also provide methods for obtaining computationally efficient gradient-based maximum a posteriori (MAP) estimates. We validate our model on synthetic data as well as on electronic health records (EHR) data from Kaiser Permanente (KP). We show that the proposed model provides better predict…

处理多变量和替代元分析中的部分缺失相关性

Dealing with partial missing correlations in multivariate and surrogate meta-analyses

针对双变量和替代元分析中部分缺失相关性的问题，提出基于Beta回归模型的多重插补方法，在随机缺失假设下通过随机过程进行插补，模拟研究表明该方法优于简单均值插补和完整案例分析。

The spatial sign covariance matrix and its application for robust correlation estimation

We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix.

Causal Patterns: Extraction of multiple causal relationships by Mixture of Probabilistic Partial Canonical Correlation Analysis

In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a mixture of simultaneous correlations or the absence of presence of a causal relationship between the elements. In multivariate statistics, partial canonical correlation analysis (PCCA) evaluates the correlation between two multivariates after subtracting the effect of the third …

Large-scale inference of correlation among mixed-type biological traits with phylogenetic multivariate probit models

Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient flexibility and computational efficiency to incorporate multiple continuous and discrete traits as data size increases. To accomplish this, we jointly model mixed-type traits by assuming latent parameters for binary outcome dimensions at the tips of an unknown tree informed by molecular sequences. This gives rise to a phylogenetic multivariate probit model. Wi…

用于聚类多变量相关结局的广义估计方程有限混合模型

Finite Mixtures of Generalized Estimating Equations for Clustering Multivariate Correlated Outcomes

针对多变量相关结局聚类问题，提出MixGEE模型，通过区域特定工作相关结构处理物种间相关性，经模拟验证可靠，应用于凯尔盖朗高原鱼类数据得到三类群落特征。

COVID-19 mortality analysis from soft-data multivariate curve regression and machine learning

A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities,…

An explicit mean-covariance parameterization for multivariate response linear regression

We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization ar…

Efficient data augmentation for multivariate probit models with panel data: An application to general practitioner decision-making about contraceptives

This article considers the problem of estimating a multivariate probit model in a panel data setting with emphasis on sampling a high-dimensional correlation matrix and improving the overall efficiency of the data augmentation approach. We reparameterise the correlation matrix in a principled way and then carry out efficient Bayesian inference using Hamiltonian Monte Carlo. We also propose a novel antithetic variable method to generate samples from the posterior distribution of the random effects and regression coefficients, resulting in significant gains in efficiency. We apply the methodolog…

用于相关分类结局的带ANOVA分解的多变量多项Logit模型

Multivariate Multinomial Logit Model with ANOVA Decomposition for Correlated Categorical Outcomes

针对医学研究中多分类结局相关性被忽略的问题，提出带ANOVA分解的多变量多项Logit模型，结合MM算法与桥惩罚项实现高效估计和变量选择，经模拟及AURORA数据验证有效。

Multivariate generalized linear mixed models for underdispersed count data

Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely applied. However, such models only allow users to model one response variable at a time. Moreover, it is not possible to directly calculate from the regression model a correlation measure between the response variables. In this article, we employed the Multivariate Generalized Linear Mixed Models framework, which allows the specification of a set of response va…

A greedy approach to sparse canonical correlation analysis

We consider the problem of sparse canonical correlation analysis (CCA), i.e., the search for two linear combinations, one for each multivariate, that yield maximum correlation using a specified number of variables. We propose an efficient numerical approximation based on a direct greedy approach which bounds the correlation at each stage. The method is specifically designed to cope with large data sets and its computational complexity depends only on the sparsity levels. We analyze the algorithm's performance through the tradeoff between correlation and parsimony. The results of numerical simu…

无金标准下评估测试准确性的潜在类别多元概率单位与潜在特质模型：一项模拟研究

Latent class multivariate probit and latent trait models for evaluating test accuracy without a gold standard: A simulation study

本文通过模拟研究比较无金标准下评估测试准确性的LC-MVP与潜在特质模型，发现LC-MVP整体性能更优且更稳健，并推荐结合自定义相关约束和先验使用LC-MVP。