A0465
Title: Graphical conditional transformation models
Authors: Matthias Herp - Georg-August-Universitaet Goettingen (Germany) [presenting]
Johannes Brachem - Georg-August-University Goettingen (Germany)
Thomas Kneib - University of Goettingen (Germany)
Michael Altenbuchinger - University Medical Center Goettingen (Germany)
Abstract: Graphical conditional transformation models (GCTMs) are proposed as a novel approach to effectively model multivariate regression data with intricate marginals and complex dependency structures non-parametrically while maintaining interpretability through the identification of conditional independencies. Multivariate conditional transformation models (MCTMs) are built upon a combination of marginal conditional transformation models(CTMs) with a conditional Gaussian copula by exchanging the copula with a custom-designed transformation. This has two major advantages. First, the GCTM can learn more complex interdependencies by using penalised splines, which also provide an efficient regularisation scheme. Second, it shows how to regularise the GCTM with a lasso penalty towards pairwise conditional independencies similar to Gaussian graphical models (GGMs). The robustness and effectiveness of the model are validated through simulations, demonstrating its ability to accurately learn parametric vine copulas, identify conditional independencies, and incorporate covariates. In addition, the model is applied to two real-world data sets. For a benchmark astrophysics data set, the model is demonstrated to compare favorably with non-parametric Vine Copulas in learning complex multivariate distributions. Similarly, in a genomics data set, it is shown that the model learns sparse undirected graphs, outperforming GGMs with transformed marginals.
