Dependence Model Assessment and Selection with DecoupleNets

Neural networks are suggested for learning a map from <i>d</i>-dimensional samples with any underlying dependence structure to multivariate uniformity in d′ dimensions. This map, termed DecoupleNet, is used for dependence model assessment and selection. If the data-generating dependence model was known, and if it was among the few analytically tractable ones, one such transformation for d′=d is Rosenblatt’s transform. DecoupleNets have multiple advantages. For example, they only require an available sample and are applicable to d′&lt;d, in particular d′=2. This allows for simpler model assessment and selection, both numerically and, because d′=2, especially graphically. A graphical assessment method has the advantage of being able to identify why, or in which region of the domain, a candidate model does not provide an adequate fit, thus, leading to model selection in particular regions of interest or improved model building strategies in such regions. Through simulation studies with data from various copulas, the feasibility and validity of this novel DecoupleNet approach is demonstrated. Applications to real world data illustrate its usefulness for model assessment and selection. Supplementary materials for this article are available online.

神经网络被用于学习一类映射：将带有任意潜在依赖结构的d维样本，映射至d′维的多元均匀分布。该映射被命名为DecoupleNet，用于依赖模型的评估与选择。若数据生成所依据的依赖模型已知，且属于少数可解析处理的模型之一，则当d′=d时，此类变换之一便是罗森布拉特变换（Rosenblatt’s transform）。DecoupleNet具有多项优势：例如，仅需可用样本即可训练，且可应用于d′<d的场景，尤其适用于d′=2的情况。这使得模型评估与选择在数值层面更为简便，且由于d′=2，还可尤其借助可视化手段完成。可视化评估方法的优势在于，能够识别候选模型拟合不佳的原因，或是具体在定义域的哪个区域出现拟合不足，进而可针对特定感兴趣区域完成模型选择，或是优化该区域内的模型构建策略。本文通过基于各类Copula函数（Copula）生成数据的模拟实验，验证了该新型DecoupleNet方法的可行性与有效性。针对真实世界数据的应用案例则展示了该方法在模型评估与选择中的实用价值。本文的补充材料可在线获取。