09-recsys

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Unformatted text preview: pu ) + λ ∑ pu +∑ qi P ,Q i u T i 2/2/2011 2 Jure Leskovec, Stanford C246: Mining Massive Datasets 27 [Bellkor Team] Want to find matrices P and Q: 2 2 2 T ∑ min training(rui − qi pu ) + λ ∑ pu +∑ qi P ,Q i u Online “stochastic” gradient decent: 2/2/2011 Initialize P and Q (random?, using SVD?) Then iterate over ratings and update qi, pu: εui = rui - qTi pu qi ← qi + γ (εui pu - λqi ) pu ← pu + γ (εui qi - λpu ) γ… learning rate Jure Leskovec, Stanford C246: Mining Massive Datasets 28 [Bellkor Team] SVD uses all of a user’s ratings to train the user’s factors But what if the user is multiple people? Different factor values may apply to movies rated by Mom vs. Dad vs. the Kids This approach computes user factors, pu , specific to the movie being predicted: rui = qiT pu(i) Vector pu(i) models behavior of u on items like i 2/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 29 [Bellkor Team] 2/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 30 [Bellkor Team] user bias movie bias Baseline predictor Separates users and movies Often overlooked Benefits from insights into users’ behavior Among the main practical contributions of the competition • • • • user-movie interaction User-movie interaction Characterizes the matching between users and movies Attracts most research in the field Benefits from algorithmic and mathematical innovations μ = overall mean rating bu = mean rating for user u bi = mean rating for movie i 2/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 31 [Bellkor Team] We have expectations on the rating by user u of movie i, even without estimating u’s attitude towards movies like i – Rating scale of user u – Values of other ratings user gave recently (day-specific mood, anchoring, multi-user accounts) 2/2/2011 – (Recent) popularity of movie i – Selection bias; related to number of ratings user gave on the same day (“frequency”) Jure Leskovec, Stanford C246: Mining Massive Datasets 32 [Bellkor Team] rui ~ µ ~ overall mean rating Example: + b u + bi + mean rating for user u mean rating for movie i user-movie interactions qTi pu Mean rating m = 3.7 You are a critical reviewer: your ratings are 1 lower than the mean: bu = -1 Star Wars gets a mean rating of 0.5 higher than average movie: bi = + 0.5 Predicted rating for you on Star Wars = 3.7 - 1 + 0.5 = 3.2 2/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 33 [Bellkor Team] Solve: min ∑ (...
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This document was uploaded on 02/26/2014 for the course CS 246 at Stanford.

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