  Learning the cumulative distribution function (CDF) of an outcome variable
conditional on a set of features remains challenging, especially in
high-dimensional settings. Conditional transformation models provide a
semi-parametric approach that allows to model a large class of conditional CDFs
without an explicit parametric distribution assumption and with only a few
parameters. Existing estimation approaches within this class are, however,
either limited in their complexity and applicability to unstructured data
sources such as images or text, lack interpretability, or are restricted to
certain types of outcomes. We close this gap by introducing the class of deep
conditional transformation models which unifies existing approaches and allows
to learn both interpretable (non-)linear model terms and more complex neural
network predictors in one holistic framework. To this end we propose a novel
network architecture, provide details on different model definitions and derive
suitable constraints as well as network regularization terms. We demonstrate
the efficacy of our approach through numerical experiments and applications.
