Related papers: Bayesian Gaussian Copula Factor Models for Mixed D…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
Missing data is a common issue in various fields such as medicine, social sciences, and natural sciences, and it poses significant challenges for accurate statistical analysis. Although numerous imputation methods have been proposed to…
Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…
Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…
This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a…
Factor models are a parsimonious way to explain the dependence of variables using several latent variables. In Gaussian 1-factor and structural factor models (such as bi-factor, oblique factor) and their factor copula counterparts, factor…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A…
Multivariate time series (MTS) data often include a heterogeneous mix of non-Gaussian distributional features (asymmetry, multimodality, heavy tails) and data types (continuous and discrete variables). Traditional MTS methods based on…
We propose a new highly flexible and tractable Bayesian approach to undertake variable selection in non-Gaussian regression models. It uses a copula decomposition for the joint distribution of observations on the dependent variable. This…
Dimension reduction techniques are among the most essential analytical tools in the analysis of high-dimensional data. Generalized principal component analysis (PCA) is an extension to standard PCA that has been widely used to identify…
We present an approach for modeling and imputation of nonignorable missing data. Our approach uses Bayesian data integration to combine (1) a Gaussian copula model for all study variables and missingness indicators, which allows arbitrary…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…