  Determinantal point processes (DPPs) are an important concept in random
matrix theory and combinatorics. They have also recently attracted interest in
the study of numerical methods for machine learning, as they offer an elegant
"missing link" between independent Monte Carlo sampling and deterministic
evaluation on regular grids, applicable to a general set of spaces. This is
helpful whenever an algorithm explores to reduce uncertainty, such as in active
learning, Bayesian optimization, reinforcement learning, and marginalization in
graphical models. To draw samples from a DPP in practice, existing literature
focuses on approximate schemes of low cost, or comparably inefficient exact
algorithms like rejection sampling. We point out that, for many settings of
relevance to machine learning, it is also possible to draw exact samples from
DPPs on continuous domains. We start from an intuitive example on the real
line, which is then generalized to multivariate real vector spaces. We also
compare to previously studied approximations, showing that exact sampling,
despite higher cost, can be preferable where precision is needed.
