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.

The development of causal prediction models is challenged by the fact that the outcome is only observable for the applied (factual) intervention and not for its alternatives (the so-called counterfactuals); in medicine we only know patients' survival for the administered drug and not for other therapeutic options. Machine learning approaches for counterfactual reasoning have to deal with both unobserved outcomes and distributional differences due to non-random treatment administration. Unsupervised domain adaptation (UDA) addresses similar issues; one has to deal with unobserved outcomes -- the labels of the target domain -- and distributional differences between source and target domain. We propose Adversarial Distribution Balancing for Counterfactual Reasoning (ADBCR), which directly uses potential outcome estimates of the counterfactuals to remove spurious causal relations. We show that ADBCR outcompetes state-of-the-art methods on three benchmark datasets, and demonstrate that ADBCR's performance can be further improved if unlabeled validation data are included in the training procedure to better adapt the model to the validation domain.

Federated Learning (FL) facilitates distributed model development to aggregate multiple confidential data sources. The information transfer among clients can be compromised by distributional differences, i.e., by non-i.i.d. data. A particularly challenging scenario is the federated model adaptation to a target client without access to annotated data. We propose Federated Adversarial Cross Training (FACT), which uses the implicit domain differences between source clients to identify domain shifts in the target domain. In each round of FL, FACT cross initializes a pair of source clients to generate domain specialized representations which are then used as a direct adversary to learn a domain invariant data representation. We empirically show that FACT outperforms state-of-the-art federated, non-federated and source-free domain adaptation models on three popular multi-source-single-target benchmarks, and state-of-the-art Unsupervised Domain Adaptation (UDA) models on single-source-single-target experiments. We further study FACT's behavior with respect to communication restrictions and the number of participating clients.