1. Intro to RecSys and CCF Brian Ackerman 1

2. Roadmap Introduction to Recommender Systems & Collaborative Filtering Collaborative Competitive Filtering 2

3. Introduction to Recommender Systems & Collaborative Filtering 3

4. Motivation Netflix has over 20,000 movies, but you may only be interested in a small number of these movies Recommender systems can provide personalized suggestions based on a large set of items such as movies – Can be done in a variety of ways, the most popular is collaborative filtering 4

5. Collaborative Filtering If two users rate a subset of items similarly, then they might rate other items similarly as well 5 Item AItem BItem CItem DItem E User 1?3453 User 21345?

6. Roadmap (RS-CF) Motivation Problem Main CF Types – Memory-based – User-based – Model-based – Regularized SVD 6

7. Problem Setting Set of users, U Set of items, I Users can rate items where r ui is user u’s rating on item i Ratings are often stored in a rating matrix – R |U|×|I| 7

8. Sample Rating Matrix Item AItem BItem CItem DItem EItem FItem GItem HItem I User 1-5-3--2-- User 24-5--4-1- User 3-4-3--2-- User 412---5-3- User 5--3-4--2- User 6-2--1--2- User 74--5--4-1 # is a user rating, - means a null entry, not rated 8

9. Problem Input – Rating matrix (R |U|×|I| ) – Active user, a (user interacting with the system) Output – Prediction for all null entries of the active user 9

10. Roadmap (RS-CF) Motivation Problem Main CF Types – Memory-based – User-based – Model-based – Regularized SVD 10

11. Main Types Memory-based – User-based* [Resnick et al. 1994] – Item-based [Sarwar et al. 2001] – Similarity Fusion (User/Item-based) [Wang et al. 2006] Model-based – SVD (Singular Value Decomposition) [Sarwar et al. 2000] – RSVD (Regularized SVD)* [Funk 2006] 11

12. User-based Find similar user’s – KNN or threshold Make prediction Item AItem BItem CItem DItem EItem FItem GItem HItem I Active?5?3??2?? User 24-5--4-1- User 3-4-3--2-- User 412---5-3- User 5--3-4--2- User 6-2--1--2- User 74--5--4-1 12

13. User-based – Similar Users Consider each user (row) to be a vector Compare each vector to find the similarity between two users – Let a be the vector for active user and u 3 be the vector for user 3 – Cosine similarity can be used to compare vectors 13

14. User-based – Similar Users KNN (k-nearest neighbors or top-k) – Only find the k most similar users Threshold – Find all users that are at most θ level of similarity Item AItem BItem CItem DItem EItem FItem GItem HItem I User 1?5-3--2-- User 24-5--4-1- User 3-4-3--2-- User 412---5-3- User 5--3-4--2- User 6-2--1--2- User 74--5--4-1 14

15. User-based – Make Prediction Weighted by similarity – Weight each similar user’s rating based on similarity to active user Similar users Prediction for active user on item i 15

16. Main Types Memory-based – User-based* [Resnick et al. 1994] – Item-based [Sarwar et al. 2001] – Similarity Fusion (User/Item-based) [Wang et al. 2006] Model-based – SVD (Singular Value Decomposition) [Sarwar et al. 2000] – RSVD (Regularized SVD)* [Funk 2006] 16

17. Regularized SVD Netflix data has 8.5 billion entries based on 17 thousand movie and.5 million users Only 100 million ratings – 1.1% of all possible ratings Why do we need to operate on such a large matrix? 17

18. Regularized SVD – Setup Let each user and item be represented by a feature vector of length k – E.g. Item A may be vector A k = [a 1 a 2 a 3 … a k ] Imagine the features for items were fixed – E.g. items are movies and each feature is a genre such as comedy, drama, etc… Features of the user vector are how well a user likes that feature 18

19. Regularized SVD – Setup Consider the movie Die Hard – Its feature vector may be i = [1 0 0] if the features are action, comedy, and drama Maybe the user has the feature vector u = [3.87 2.64 1.32] We can try to predict a user’s rating using the dot product of these two vectors – r’ ui = u ∙ i = [1 0 0] ∙ [3.87 2.64 1.32] = 3.87 19

20. Regularized SVD – Goal Try to find values for each item vector that work for all users Try to find value for each user vector that can produce the actual rating when taking the dot product with the item vector Minimizing the difference between the actual and predicted (based on dot product) rating 20

21. Regularized SVD – Setup In reality, we cannot choose k to be large enough for a fixed number of features – There are too many to consider (e.g. genre, actors, directors, etc…) Usually k is only 25 to 50 which reduces the total size of the matrices to only roughly 25 million to 50 million (compared to 8.5 billion) Because of the size of k, the values in the vectors are NOT directly tied to any feature 21

22. Regularized SVD – Goal Let u be a user, i be an item, r ui is a rating by user u on item i where R is the set of all ratings, and φ u, φ i are the vectors At first thought, it seems simple to have the following optimization goal 22

23. Regularized SVD – Overfitting Problem is overfitting of the features – Solved by regularization 23

24. Regularized SVD – Regularization Introduce a new optimization goal including a term for regularization Minimizing the magnitude of the feature vectors – Controlled by fixed parameters λ u and λ i 24

25. Regularized SVD Many improvements have been proposed to improve the regularized optimization goal – RSVD2/NSVD1/NSVD2 [Paterek 2007]: added term for user bias and a term for item bias, minimize number of parameters – Integrated Neighborhood SVD++ [Koren 2008]: used a neighborhood-based approach to RSVD 25

26. Roadmap Introduction to Recommender Systems & Collaborative Filtering Collaborative Competitive Filtering 26

27. Collaborative Competitive Filtering: Learning Recommender Using Context of User Choice Georgia Tech and Yahoo! Labs Best Student Paper at SIGIR’11 27

28. Motivation A user may be given 5 random movies and chooses Die Hard – This tells us the user prefers action movies A user may be given 5 actions movies and chooses Die Hard over Rocky and Terminator – This tells us the user prefers Bruce Willis 28

29. Roadmap (CCF) Motivation Problem Setting & Input Techniques Extensions 29

30. Problem Setting Set of users, U Set of items, I Each user interaction has an offer set O and a decision set D Each user interaction is stored as a tuple (u, O, D) where D is a subset of O 30

31. CCF Input Item AItem BItem CItem DItem EItem FItem GItem HItem I U1-S11--- U1-S2--1- U1-S3---1 U2-S1-1--- U2-S2-1-- U3-S1---1 U3-S2---1 1 means user interaction, - means it was in the offer set 31

32. Roadmap (CCF) Motivation Problem Setting & Input Techniques Extensions 32

33. Local Optimality of User Choice Each item has a potential revenue to the user which is r ui Users also consider the opportunity cost (OC) when deciding potential revenue – OC is what the user gives up for making a given decision OC is c ui = max( i’ | i’ in O \ i) Profit is π ui = r ui – c ui 33

34. Local Optimality of User Choice A user interaction is an opportunity give and take process – User is given a set of opportunities – User makes a decision to select one of the many opportunities – Each opportunity comes with some revenue (utility or relevance) 34

35. Competitive Collaborative Filtering Local optimality constraint – Each item in the decision set has a revenue higher than those not in the decision set – Problem becomes intractable with only this constraint, no unique solution 35

36. CCF – Hinge Model Optimization goal – Minimize error (ξ, slack variable) & model complexity 36

37. CCF – Hinge Model Find average potential utility – Average utility of non-chosen items Constraints – Chosen items have a higher utility – e ui is an error term 37

38. CCF – Hinge Model Optimization Goal – Assume ξ is 0 Average Relevance of Non-chosen Items 38

39. CCF – How to use results We can predict the relevance of all items based on user and item vectors – Can set threshold if more than one item can be chosen (e.g. θ >.9 implies action) ItemUser ActionPredicted Relevance A1.98 B-.93 C-.56 D-.25 E-.11 39

40. Roadmap (CCF) Motivation Problem Setting & Input Techniques Extensions 40

41. Extensions Sessions without a response – User does not take any opportunity Adding content features – Fixed features for each item rather than a limited number of parameters to improve accuracy of new item prediction 41