  Machine Learning research, as most of Statistics, heavily relies on the
concept of a data-generating probability distribution. As data points are
thought to be sampled from such a distribution, we can learn from observed data
about this distribution and, thus, predict future data points drawn from it
(with some probability of success). Drawing on scholarship across disciplines,
we here argue that this framework is not always a good model. Not only do such
true probability distributions not exist; the framework can also be misleading
and obscure both the choices made and the goals pursued in machine learning
practice. We suggest an alternative framework that focuses on finite
populations rather than abstract distributions; while classical learning theory
can be left almost unchanged, it opens new opportunities, especially to model
sampling. We compile these considerations into five reasons for modelling
machine learning -- in some settings -- with finite distributions rather than
generative distributions, both to be more faithful to practice and to provide
novel theoretical insights.
