  We present a deep transformation model for probabilistic regression. Deep
learning is known for outstandingly accurate predictions on complex data but in
regression tasks, it is predominantly used to just predict a single number.
This ignores the non-deterministic character of most tasks. Especially if
crucial decisions are based on the predictions, like in medical applications,
it is essential to quantify the prediction uncertainty. The presented deep
learning transformation model estimates the whole conditional probability
distribution, which is the most thorough way to capture uncertainty about the
outcome. We combine ideas from a statistical transformation model (most likely
transformation) with recent transformation models from deep learning
(normalizing flows) to predict complex outcome distributions. The core of the
method is a parameterized transformation function which can be trained with the
usual maximum likelihood framework using gradient descent. The method can be
combined with existing deep learning architectures. For small machine learning
benchmark datasets, we report state of the art performance for most dataset and
partly even outperform it. Our method works for complex input data, which we
demonstrate by employing a CNN architecture on image data.
