Randomization, Martingales and Additional Information in Inductive Inference

Abstract

Finite identification, sometimes called “one shot learning,” is the most basic identification type studied in Inductive Inference. There are several ways to generalize this notion. One of the more popular generalizations is to consider identification in the limit, as opposed to one attempt. We other generalization that we consider are randomized finite identification and finite identification with an additional information. We prove that these lines of generalization are not merely independent (neither one majorize the other one) but also incompatible (simultaneous generalization into two of these directions provides no generalization at all).