[Feature]: prevent empty sets (keep conformal validity, lose upper bound tight coverage)

[lmossina]

While working with conformal classification with JD, we realized that it makes sense to be able to force non-empty prediction sets, at least from an operational point of view.

For example, in classification via softmax, this corresponds to always including the class whose score is highest (even if very low). In the case of (R)APS, this means bypassing the randomization step.

In the RAPS paper, here is the explication of the phenomenon:

• https://openreview.net/pdf?id=eNdiU_DbM9#appendix.B

Here also the detail of the algo with and without the randomization:

• Algorithms 2 & 3: If $rand == False$, than do not do randomization.
• Notice that randomization is both in computation of nonconformity scores and prediction, so we must take care of both.

I reckon we could achieve this simply by adding a flag to the class, such as at instantiation:

• aps_cp = RAPS(class_predictor, [...], avoid_empty_sets=True)