Vine copulas are sophisticated models for multivariate distributions and are increasingly used in machine learning. To facilitate their integration into modern ML pipelines, we introduce the vine computational graph, a DAG that abstracts the multilevel vine structure and associated computations. On this foundation, we devise new algorithms for conditional sampling, efficient sampling-order scheduling, and constructing vine structures for customized conditioning variables. We implement these ideas in torchvinecopulib, a GPU-accelerated Python library built upon PyTorch, delivering improved scalability for fitting, sampling, and density evaluation. Our experiments illustrate how gradient flowing through the vine can improve Vine Copula Autoencoders and that incorporating vines for uncertainty quantification in deep learning can outperform MC-dropout, deep ensembles, and Bayesian Neural Networks in sharpness, calibration, and runtime. By recasting vine copula models as computational graphs, our work connects classical dependence modeling with modern deep-learning toolchains and facilitates the integration of state-of-the-art copula methods in modern machine learning pipelines.

We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.

A new framework based on the theory of copulas is proposed to address semisupervised domain adaptation problems. The presented method factorizes any multivariate density into a product of marginal distributions and bivariate copula functions. Therefore, changes in each of these factors can be detected and corrected to adapt a density model accross different learning domains. Importantly, we introduce a novel vine copula model, which allows for this factorization in a non-parametric manner. Experimental results on regression problems with real-world data illustrate the efficacy of the proposed approach when compared to state-of-the-art techniques.

A vine copula model is a flexible high-dimensional dependence model which uses only bivariate building blocks. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. In this work, we formulate a vine structure learning problem with both vector and reinforcement learning representation. We use neural network to find the embeddings for the best possible vine model and generate a structure. Throughout experiments on synthetic and real-world datasets, we show that our proposed approach fits the data better in terms of log-likelihood. Moreover, we demonstrate that the model is able to generate high-quality samples in a variety of applications, making it a good candidate for synthetic data generation.

Copulas and Rank Order Correlation are two ways to model and/or explain the dependence between 2 or more variables. Historically used in biology and epidemiology, copulas have gained acceptance and prominence in the financial services sector. In this article we are going to untangle what correlation and copulas are and how they relate to each other. In order to prepare a summary overview, I had to read painfully dry material… but the results is a practical guide to understanding copulas and when you should consider them. I lay no claim to being a stats expert or mathematician… just a risk analysis professional. So my approach to this will be pragmatic.

We develop multivariate copulas for modeling multiple joint distributions of wind speeds at a wind farm site and neighboring wind source. A ndimensional Gaussian copula and multiple copula graphical models enhance the quality of the prediction site distribution. The models, in comparison to multiple regression, achieve higher accuracy and lower cost because they require less sensing data.

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is independent from its conditioning variables. In this paper, we relax this assumption by discovering the latent functions that specify the shape of a conditional copula given its conditioning variables. We learn these functions by following a Bayesian approach based on sparse Gaussian processes with expectation propagation for scalable, approximate inference. Experiments on real-world datasets show that, when modeling all conditional dependencies, we obtain better estimates of the underlying copula of the data.

A new framework based on the theory of copulas is proposed to address semi-supervised domain adaptation problems. The presented method factorizes any multivariate density into a product of marginal distributions and bivariate copula functions. Therefore, changes in each of these factors can be detected and corrected to adapt a density model across different learning domains. Importantly, we introduce a novel vine copula model, which allows for this factorization in a non-parametric manner. Experimental results on regression problems with real-world data illustrate the efficacy of the proposed approach when compared to state-of-the-art techniques.

We utilize the ensemble of trees framework, a tractable mixture over superexponential number of tree-structured distributions [1], to develop a new model for multivariate density estimation. The model is based on a construction of treestructured copulas - multivariate distributions with uniform on [0, 1] marginals.

The model is based on a construction of tree-structured copulas -- multivariate distributions with uniform on [07 1] marginals.