  The parameters of a machine learning model are typically learned by
minimizing a loss function on a set of training data. However, this can come
with the risk of overtraining; in order for the model to generalize well, it is
of great importance that we are able to find the optimal parameter for the
model on the entire population -- not only on the given training sample. In
this paper, we construct valid confidence sets for this optimal parameter of a
machine learning model, which can be generated using only the training data
without any knowledge of the population. We then show that studying the
distribution of this confidence set allows us to assign a notion of confidence
to arbitrary regions of the parameter space, and we demonstrate that this
distribution can be well-approximated using bootstrapping techniques.
