Interpretable machine learning and generative modeling with mixed tabular data - advancing methodology from the perspective of statistics

Explainable artificial intelligence or interpretable machine learning techniques aim to shed light on the behavior of opaque machine learning algorithms, yet often fail to acknowledge the challenges real-world data imposes on the task. Specifically, the fact that empirical tabular datasets may consist of both continuous and categorical features (mixed data) and typically exhibit dependency structures is frequently overlooked. This work uses a statistical perspective to illuminate the far-reaching implications of mixed data and dependency structures for interpretability in machine learning. Several interpretability methods are advanced with a particular focus on this kind of data, evaluating their performance on simulated and real data sets. Further, this cumulative thesis emphasizes that generating synthetic data is a crucial subroutine for many interpretability methods. Therefore, this thesis also advances methodology in generative modeling concerning mixed tabular data, presenting a tree-based approach for density estimation and data generation, accompanied by a user-friendly software implementation in the Python programming language.