The diagram above shows a very broad viewpoint of learning theory.
|Past->Past||Some prediction algorithm A does almost as well as any of a set of algorithms.||Weighted Majority|
|Past->Future||Assuming independent samples, past performance predicts future performance.||PAC analysis, ERM analysis|
|Future->Future||Future prediction performance on subproblems implies future prediction performance using algorithm A.||ECOC, Probing|
A basic question is: Are there other varieties of statements of this type? Avrim noted that there are also “arrows between arrows”: generic methods for transforming between Past->Past statements and Past->Future statements. Are there others?