Collaborative Filtering with Temporal Dynamics

1. Collaborative Filtering with Temporal Dynamics Yehuda Koren

2. Recommender systems We Know What You OughtTo Be Watching This Summer

3. Collaborative filtering • Recommend items based on past transactions of users • Specific data characteristics are irrelevant • Domain-free • Can identify elusive aspects • Two popular approaches: • Matrix factorization • Neighborhood

4. Movie rating data Training data Test data

5. erroneous accurate Achievable RMSEs on the Netflix data Global average: 1.1296 Find better items User average: 1.0651 Movie average: 1.0533 Personalization Cinematch: 0.9514; baseline “Algorithmics” Static neighborhood: 0.9002 Static factorization: 0.8911 Time effects Leader: 0.8558; 10.05% improvement Inherent noise: ????

6. Something Happened in Early 2004… 2004

7. Are movies getting better with time?

8. Multiple sources of temporal dynamics • Item-side effects: • Product perception and popularity are constantly changing • Seasonal patterns influence items’ popularity • User-side effects: • Customers ever redefine their taste • Transient, short-term bias; anchoring • Drifting rating scale • Change of rater within household

9. Temporal dynamics - challenges • Multiple sources: Both items and users are changing over time • Multiple targets: Each user/item forms a unique time series  Scarce data per target • Inter-related targets: Signal needs to be shared among users – foundation of collaborative filtering  cannot isolate multiple problems  Common “concept drift” methodologies won’t hold.E.g., underweighting older instances is unappealing

10. Basic matrix factorization model users ~ items users ~ items A rank-3 SVD approximation

11. Estimate unknown ratings as inner-products of factors: users ? ~ items users ~ items A rank-3 SVD approximation

12. Estimate unknown ratings as inner-products of factors: users ? ~ items users ~ items A rank-3 SVD approximation

13. Estimate unknown ratings as inner-products of factors: users 2.4 ~ items users ~ items A rank-3 SVD approximation

14. Matrix factorization model Properties: • SVD isn’t defined when entries are unknown  use specialized methods • Can easily overfit, sensitive to regularization • Need to separate main effects… ~

15. Baseline predictors • Mean rating: 3.7 stars • The Sixth Sense is 0.5 stars above avg • Joe rates 0.2 stars below avg Baseline prediction:Joe will rate The Sixth Sense4 stars No user-item interaction

16. Factor model correction • Both The Sixth Sense and Joe are placed high on the “Supernatural Thrillers” scale Adjusted estimate:Joe will rate The Sixth Sense4.5 stars

17. Matrix factorization with biases Baseline predictors: μ– global average bu – bias of u bi – bias of i User-item interaction: pu – user u‘sfactors qi – item i‘sfactors Minimization problem: regularization

18. Addressing temporal dynamics • Factor model conveniently allows separately treating different aspects • We observe changes in: • Rating scale of individual users • Popularity of individual items • User preferences Baseline predictors User factors

19. Parameterizing the model • Use functional forms: bu(t)=f(u,t), bi(t)=g(i,t), pu(t)=h(u,t) • Need to find adequate f(), g(), h() • General guidelines: • Items show slower temporal changes • Users exhibit frequent and sudden changes • Factors –pu(t)– are expensive to model • Gain flexibility by heavily parameterizing the functions

20. erroneous accurate Achievable RMSEs on the Netflix data Global average: 1.1296 Find better items User average: 1.0651 Movie average: 1.0533 Personalization Cinematch: 0.9514; baseline “Algorithmics” Static neighborhood: 0.9002 Static factorization: 0.8911 Time effects Dynamic factorization: 0.8794 Grand Prize: 0.8563; 10% improvement Inherent noise: ????

21. Neighborhood-based CF • Earliest and most common collaborative filtering method • Derive unknown ratings from those of “similar” items (item-item variant)

22. Neighborhood modeling Use item-item weights - wij- to relate items: Need to estimate rating of user u for item i Deviation from baseline estimate for item j Baseline predictor Weight from j to i Set of items rated by u constants learned from the data through optimization

23. Optimizing the model Minimize the squared error function:

24. Making the model time-aware • A popular scheme – instance weighting:decay the significance of outdated events within cost function: time decay Don’t do this!

25. Why instance weighting isn’t suitable? • Not enough data per user – need to exploit all signal, including old one • The learnt parameters – wij– represent time invariant item-item relations. Can be also deduced from older actions. • Two items are related when users rated them similarly within a short timeframe, even if this happened long ago • How to do it right?

26. Time-aware neighborhood model • Decay item-item relations based on time distance • User-specific decay rate; controlled by βu • All past user behavior is equally considered, through cost function:

27. erroneous accurate Temporal neighborhood model delivers same relative RMSE improvement (0.0117) as temporal factor model (!) Global average: 1.1296 Find better items User average: 1.0651 Movie average: 1.0533 Personalization Cinematch: 0.9514; baseline “Algorithmics” Static neighborhood:0.9002 Static factorization: 0.8911 Dynamic neighborhood: 0.8885 Time effects Dynamic factorization: 0.8794 Grand Prize: 0.8563; 10% improvement Inherent noise: ????

28. Lessons • Modeling temporal effects is significant in improving recommenders accuracy • Allow multiple time drifting patterns across users and items • Integrate allusers within a single model to allow crucial cross-user collaboration • Model user behavior along full history, do not over-emphasize recent actions • Separate long term values, while excluding transient fluctuations from the model • Sudden, single-day effects are significant • Modeling past temporal fluctuations helps in predicting future behavior, even though we do not extrapolate future temporal dynamics

29. Yehuda Koren Yahoo! Research yehuda@yahoo-inc.com