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.

翻译：我们提出将Copula密度估计重新解释为一个判别式任务。在这一新颖的估计框架下，我们训练一个分类器来区分来自联合密度的样本与来自独立边缘分布乘积的样本，并在此过程中恢复Copula密度。我们推导了著名的Copula类别与在我们的解释中自然产生的分类问题之间的等价关系。此外，我们证明了我们的估计器能够达到类似于最大似然估计的理论保证。通过建立与密度比估计的联系，我们得以受益于该领域丰富的文献和可用模型。在实证研究中，我们通过对真实和高维数据集的Copula进行估计，展示了我们方法的适用性，其在密度评估和采样方面均优于其他竞争性Copula估计器。