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

A time series is an extremely wide-spread type of empirical data: a (potentially
multivariate) set of observations that evolves over a univariate and thus ordered
index space—time. Examples include stock prices, inventory levels, sports
statistics, sensor readings in scientific equipment, cars and machinery, and many
more. Time series often require real-time processing, and can potentially be
infinitely long. But their univariate domain also allows for a crucial property
of the model: Markovianity, the ability to locally store all aspects of the model
necessary for inference in a time-local memory of fixed and finite size. This
course introduces a range of models and algorithms for efficient and flexible
inference in time series. Starting from famous concepts from the areas of signal
processing and control, we will move to recent and contemporary models
for structured, high-dimensional, non-linear and irregular time series. Alongside
data and models, efficient algorithms for approximate inference are a core
focus.
Apart from mathmatical derivations, the exercises put a focus on practical
programming. In particular, they contain implementations of some content of
the lectures.

Students develop an understanding for key algorithmic and modelling challenges
in the analysis of, and practical inference with time-ordered processes and
data. They can implement and debug basic and advanced models for such data,
including for production-level, large-scale applications, and for areas demanding
high quality predictions, such as scientific analysis. Apart from mathmatical
derivations, the exercises put a focus on practical programming. In particular,
they contain implementations of some content of the lectures.

Literature will be listed at the beginning of the semester.