用可定制变换建模复杂多变量依赖，兼具解释性与高效正则化。
Graphical Transformation Models
- 用自定义变换替代高斯拷贝函数，灵活捕捉复杂依赖关系。
- 通过惩罚样条实现高效正则化，准确识别条件独立性。
- 在天体物理数据上优于非参数藤蔓拷贝函数，适合高维依赖建模。
图变换模型（GTMs）是一种新型半参数方法，用于有效建模具有复杂边缘分布和复杂依赖结构的多变量数据，同时通过识别变化的条件独立性保持可解释性。GTMs 通过将高斯拷贝函数替换为自定义的多变量变换来扩展多变量变换模型，具有两大优势：首先，利用惩罚样条可捕捉更复杂的相互依赖关系，同时提供高效的正则化方案；其次，我们展示了如何使用 lasso 正则化近似地将 GTMs 压向成对条件独立性，类似于高斯图模型。通过模拟验证了模型的鲁棒性和有效性，展示其准确学习复杂依赖并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，在学习复杂多变量分布方面表现优于非参数藤蔓拷贝函数。
原文摘要 · Abstract (English)
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, 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 towards pairwise conditional independencies using a lasso penalty, akin to Gaussian graphical models. The model's robustness and effectiveness are validated through simulations, showcasing its ability to accurately learn complex dependencies 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.
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