  The application of machine learning to physics problems is widely found in
the scientific literature. Both regression and classification problems are
addressed by a large array of techniques that involve learning algorithms.
Unfortunately, the measurement errors of the data used to train machine
learning models are almost always neglected. This leads to estimations of the
performance of the models (and thus their generalisation power) that is too
optimistic since it is always assumed that the target variables (what one wants
to predict) are correct. In physics, this is a dramatic deficiency as it can
lead to the belief that theories or patterns exist where, in reality, they do
not. This paper addresses this deficiency by deriving formulas for commonly
used metrics (both for regression and classification problems) that take into
account measurement errors of target variables. The new formulas give an
estimation of the metrics which is always more pessimistic than what is
obtained with the classical ones, not taking into account measurement errors.
The formulas given here are of general validity, completely model-independent,
and can be applied without limitations. Thus, with statistical confidence, one
can analyze the existence of relationships when dealing with measurements with
errors of any kind. The formulas have wide applicability outside physics and
can be used in all problems where measurement errors are relevant to the
conclusions of studies.
