Related papers: Non-iterative Gaussianization
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
Key to effective generic, or "black-box", variational inference is the selection of an approximation to the target density that balances accuracy and speed. Copula models are promising options, but calibration of the approximation can be…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
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…
We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
We present a framework to compute non-Gaussian likelihoods for two-point correlation functions. The non-Gaussianity is most pronounced on large scales that will be well-measured by stage-IV weak-lensing surveys. We show how such a…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint…
The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distributions. However, this kind of model can potentially be too restrictive since it expresses a…
We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the…
Instance-wise feature selection and ranking methods can achieve a good selection of task-friendly features for each sample in the context of neural networks. However, existing approaches that assume feature subsets to be independent are…
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques…
Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…
In this work we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a…
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 propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…