I've been reading few papers on how Netflix prize was won. One of the methods used by the winning team was to split the user-movie rating into various bias. For example, the movie rating by an user would be broken down into average rating of all movies + user bias + movie bias + user-movie interaction. I'm just wondering how this kind of split would solve the duplication of bias as in user-movie bias would definitely contain a part of user bias. The other question is, lets assume that the original rating for movie X from a Person Y was 4. Let the average rating across movie be 3. Let assume that Y always rate +1 more than average (across all movies) and X was always rated +1 more than average. Now if we would combine we would get a rating of >= 5 (assuming user-movie interaction to be positive). How could we handle these kinds of scenarios?
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