  Recently proposed quasi-Bayesian (QB) methods initiated a new era in Bayesian
computation by directly constructing the Bayesian predictive distribution
through recursion, removing the need for expensive computations involved in
sampling the Bayesian posterior distribution. This has proved to be
data-efficient for univariate predictions, but extensions to multiple
dimensions rely on a conditional decomposition resulting from predefined
assumptions on the kernel of the Dirichlet Process Mixture Model, which is the
implicit nonparametric model used. Here, we propose a different way to extend
Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem
by decomposing the predictive distribution into one-dimensional predictive
marginals and a high-dimensional copula. Thus, we use the efficient recursive
QB construction for the one-dimensional marginals and model the dependence
using highly expressive vine copulas. Further, we tune hyperparameters using
robust divergences (eg. energy score) and show that our proposed Quasi-Bayesian
Vine (QB-Vine) is a fully non-parametric density estimator with \emph{an
analytical form} and convergence rate independent of the dimension of data in
some situations. Our experiments illustrate that the QB-Vine is appropriate for
high dimensional distributions ($\sim$64), needs very few samples to train
($\sim$200) and outperforms state-of-the-art methods with analytical forms for
density estimation and supervised tasks by a considerable margin.
