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.

翻译：最近提出的拟贝叶斯方法通过递归直接构建贝叶斯预测分布，消除了对贝叶斯后验分布进行采样所需的高昂计算成本，从而开启了贝叶斯计算的新纪元。该方法已被证明在单变量预测中具有数据高效性，但其向多维度的扩展依赖于狄利克雷过程混合模型核函数的预定义假设所产生的条件分解，而该模型正是所使用的隐式非参数模型。本文提出了一种通过Sklar定理将拟贝叶斯预测扩展至高维度的新方法：将预测分布分解为一维预测边缘分布和一个高维联结函数。因此，我们使用高效的递归拟贝叶斯构造处理一维边缘分布，并利用高表达能力的藤蔓联结函数对依赖关系进行建模。此外，我们采用鲁棒散度（如能量评分）调整超参数，并证明所提出的拟贝叶斯藤蔓模型是一种具有解析形式的完全非参数密度估计器，在某些情况下其收敛速率与数据维度无关。实验表明，拟贝叶斯藤蔓模型适用于高维分布（约64维），仅需极少训练样本（约200个），且在密度估计和监督任务的解析方法中显著优于现有最优方法。