The efficiency of probabilistic predictors

Efficiency is a performance metric used to evaluate probabilistic predictors. It measures how precise or informative the prediction intervals or regions are. In other words, efficiency indicates how tight or narrow the predicted probability distributions are. Smaller intervals or regions are considered more efficient, as they convey more certainty about the predicted outcomes.

While validity focuses on ensuring that the error rate is controlled, efficiency assesses the usefulness and precision of the predictions. An efficient predictor provides more specific information about the possible outcomes, whereas a less efficient predictor generates wider intervals or regions, resulting in less precise information.

There is an inherent trade-off between validity and efficiency. A conformal predictor can always achieve perfect validity by outputting very wide prediction sets that encompass all possible outcomes. However, this lacks efficiency...