Graphical Transformation Models
This provides a more flexible semiparametric method for multivariate data analysis in fields like astrophysics, though it appears incremental as an extension of existing transformation models.
The authors introduced Graphical Transformation Models (GTMs) to model multivariate data with complex marginals and dependencies semiparametrically while maintaining interpretability through conditional independencies. They validated GTMs via simulations showing accurate dependency learning and applied them to an astrophysics dataset where GTMs outperformed non-parametric vine copulas.
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.