Four Facets of Forecast Felicity: Calibration, Predictiveness,
  Randomness and Regret
Rabanus Derr Robert C. Williamson
Machine learning is about forecasting. Forecasts, however, obtain their
usefulness only through their evaluation. Machine learning has traditionally
focused on types of losses and their corresponding regret. Currently, the
machine learning community regained interest in calibration. In this work, we
show the conceptual equivalence of calibration and regret in evaluating
forecasts. We frame the evaluation problem as a game between a forecaster, a
gambler and nature. Putting intuitive restrictions on gambler and forecaster,
calibration and regret naturally fall out of the framework. In addition, this
game links evaluation of forecasts to randomness of outcomes. Random outcomes
with respect to forecasts are equivalent to good forecasts with respect to
outcomes. We call those dual aspects, calibration and regret, predictiveness
and randomness, the four facets of forecast felicity.