Lecture 18 and Shapley value

[yaser]

This is a clarification of the last point in Lecture 18 that raised some questions

Q: At the end of the lecture, the contribution of an individual hypothesis to the overall performance of a blend of hypotheses was discussed. Shouldn't that contribution be determined by the Shapley value?

A: What was discussed in the lecture applies to the incremental value of an added hypothesis to an existing blend, such as the case when the Netflix prize team solicited new contributions to its existing blended solution. The Shapley value provides the correct value in the symmetric case, where all players enter the game at the same time so to speak. For instance, according to the Shapely value, two identical hypotheses in a blend share the reward for that hypothesis, rather than having the one that entered late get no reward for being redundant, as would have been the case in the Netflix team.