Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures non-parametrically, while maintaining interpretability through the identification of varying conditional independencies. GTMs extend multivariate transformation models by replacing the Gaussian copula with a custom-designed multivariate transformation, offering two major advantages. Firstly, GTMs can capture more complex interdependencies using penalized splines, which also provide an efficient regularization scheme. Secondly, we demonstrate how to approximately regularize GTMs using a lasso penalty towards pairwise conditional independencies, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn parametric vine copulas and identify conditional independencies. Additionally, the model is applied to a benchmark astrophysics dataset, where the GTM demonstrates favorable performance compared to non-parametric vine copulas in learning complex multivariate distributions.

翻译：图形变换模型（GTMs）作为一种新颖方法被提出，旨在以非参数方式有效建模具有复杂边缘分布和依赖结构的多元数据，同时通过识别变化的条件独立性保持模型的可解释性。GTMs通过将高斯连接函数替换为定制设计的多元变换，扩展了多元变换模型，具有两大优势。首先，GTMs能够利用惩罚样条捕获更复杂的相互依赖关系，同时提供有效的正则化方案。其次，我们展示了如何通过类似高斯图模型的lasso惩罚向成对条件独立性进行近似正则化。通过仿真实验验证了模型的鲁棒性和有效性，展示了其准确学习参数化藤连接函数和识别条件独立性的能力。此外，该模型应用于基准天体物理学数据集，结果表明GTMs在学习复杂多元分布方面相较于非参数藤连接函数表现出更优的性能。