  Every uncalibrated classifier has a corresponding true calibration map that
calibrates its confidence. Deviations of this idealistic map from the identity
map reveal miscalibration. Such calibration errors can be reduced with many
post-hoc calibration methods which fit some family of calibration maps on a
validation dataset. In contrast, evaluation of calibration with the expected
calibration error (ECE) on the test set does not explicitly involve fitting.
However, as we demonstrate, ECE can still be viewed as if fitting a family of
functions on the test data. This motivates the fit-on-the-test view on
evaluation: first, approximate a calibration map on the test data, and second,
quantify its distance from the identity. Exploiting this view allows us to
unlock missed opportunities: (1) use the plethora of post-hoc calibration
methods for evaluating calibration; (2) tune the number of bins in ECE with
cross-validation. Furthermore, we introduce: (3) benchmarking on pseudo-real
data where the true calibration map can be estimated very precisely; and (4)
novel calibration and evaluation methods using new calibration map families PL
and PL3.
