Written exam (in case of a small number of participants: oral tests)

Probabilistic inference is a foundation of scientific reasoning, statistics, and
machine learning. The lecture course begins with a general introduction to basic
principles (rules of probability theory, graphical models), then covers the
probabilistic view on many standard settings, like supervised regression and
classification, and unsupervised dimensionality reduction and clustering. In a
parallel thread through the lecture, we will also encounter a number of popular
algorithms for inference in probabilistic models, including exact inference
in Gaussian models, sampling, and free-energy methods. At specific points,
connections and differences to non-probabilistic frameworks will be made.
Apart from mathmatical derivations, the exercises put a focus on practical
programming. In particular, they contain implementations of some content of
the lectures.

Students gain an intuitive, as well as a mathematical and algorithmic understanding
of probabilistic reasoning. They acquire a mental toolbox of probabilistic
models for various problem classes, along with the algorithms required
for their concrete implementation. Over the course of the lecture, they also
become proficient in the fundamental concept of uncertainty, and the philosophical
challenges and pitfalls associated with it. They are empowered to build,
analyse, and use their own probabilistic models for concrete use cases.

Literature will be listed at the beginning of the semester. / Standard undergraduate knowledge of mathematics is required, to the extent
that is provided, for example, by the course on Mathematics for Machine Learning
(ML 4101).