CoFi-points: Collaborative Filtering via Pointwise Preference Learning on User/Item-Set Lin Li 1 , 2 , Weike Pan 1 , 2 , ∗ and Zhong Ming 1 , 2 , ∗ lilin20171@email.szu.edu.cn, { panweike,mingz } @szu.edu.cn 1 College of Computer Science and Software Engineering Shenzhen University, Shenzhen, China 2 National Engineering Laboratory for Big Data System Computing Technology Shenzhen University, Shenzhen, China Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 1 / 38
Introduction Problem Definition One-Class Collaborative Filtering (OCCF) Input : (user, item) pairs, e.g., an observed (user, item) pair ( u , i ) denotes that a user u has a relatively positive feedback on an item i . Goal : recommend a personalized ranked list of unobserved items from I\I u for each user u . Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 2 / 38
Introduction Challenges Data : lack of negative feedback in the training data. Model : how to facilitate effective pointwise preference learning for ranking-oriented tasks without the expense of accuracy. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 3 / 38
Introduction Overall of Our Solution We first propose a new preference assumption for implicit 1 feedback, i.e., pointwise preference assumption on user/item-set. We then develop a novel recommendation solution with two 2 specific algorithms based on the proposed assumption, i.e. CoFi-points: collaborative filtering via pointwise preference learning on user/item-set. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 4 / 38
Introduction Advantages of Our Solution Our solution inherits the merit of preferences defined on a set of users or items, which are empirically shown more accurate than that on a single user or item only, and yield substantial improvements in handling uncertainty of the implicit feedback Our solution adopts the pointwise preference assumption with different strategies on observed and unobserved user/item-set, which transforms the limitation into an advantage we can benefit from. Our pointwise scheme naturally facilitates better adaptability and extensibility in comparison with the pairwise one. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 5 / 38
Introduction Notations (1/2) Table: Notations and explanations n number of users m number of items U = { 1 , 2 , .., n } the whole set of users I = { 1 , 2 , .., m } the whole set of items u ∈ U user ID i , j ∈ I item ID R = { ( u , i ) } training data of observed pairs R te = { ( u , i ) } test data of observed pairs I u the set of items that have been interacted with by u P ⊆ I u a randomly sampled observed item-set A ⊆ I\I u a randomly sampled unobserved item-set ˆ r ui estimated preference of u to i ˆ r u P estimated preference of u to P ˆ r u A estimated preference of u to A Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 6 / 38
Introduction Notations (2/2) Table: Notations and explanations (cont.) U i the set of users who have interacted with item i G ⊆ U i a randomly sampled observed user-set interacted with item i ˆ r G i estimated preference of user-set G to item i ˆ r G ui estimated fused preference of user-set G and user u to item i U u · ∈ R 1 × d latent vector of user u V i · ∈ R 1 × d latent vector of item i b u ∈ R bias of user u b i ∈ R bias of item i sampling ratio for unobserved pairs ρ learning rate γ T iteration number Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 7 / 38
Method Existing Preference Assumptions Pointwise preference assumption on item: r ui = 1 , r uj = 0 , i ∈ I u , j ∈ I\I u . (1) Pairwise preference assumption on item: r ui > r uj , i ∈ I u , j ∈ I\I u . (2) Pairwise preference assumption on item-set: r u P > r u A , P ⊆ I u , A ⊆ I\I u . (3) Pairwise preference assumption on user-set: r G ui > r uj , i ∈ I u , G ⊆ U i , j ∈ I\I u . (4) Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 8 / 38
Method Illustration John observed items unobserved items Jacky Rebecca Pairwise preference learning over items: (John, Forrest Gump ) (John, Prince of Egypt ) Point preference learning over items: (John, Forrest Gump ) (John, Prince of Egypt ) Pairwise preference learning over item-set: (John, < Forrest Gump, A Beautiful Mind> ) (John, < Prince of Egypt, The Matrix> ) Pointwise preference learning over item-set: (John, Prince of Egypt ) (John, < Forrest Gump, A Beautiful Mind> ) (John, The Matrix ) Pairwise preference learning over user-set: (John, Prince of Egypt ) (<John, Jacky, Rebecca>, Forrest Gump ) (John, The Matrix ) Pointwise preference learning over user-set: (John, Prince of Egypt ) (<John, Jacky, Rebecca>, Forrest Gump ) (John, The Matrix ) Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 9 / 38
Method Pointwise Preference Assumption on Item-set (1/2) It is more natural to assume that a randomly sampled observed set is liked by a certain user, because it is more likely for a set to include some items that are liked by the user. If John is a devoted fan of inspirational movies while Rebecca is an adventurer who enjoys diverse ones, then it would be obvious that Forrest Gump means much more to John compared with Rebecca. But a typical pointwise assumption assumes Forrest Gump contributes the same to John’s and Rebecca’s movie taste, i.e., (John, Forrest Gump ) → 1 and (Rebecca, Forrest Gump ) → 1. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 10 / 38
Method Pointwise Preference Assumption on Item-set (2/2) Our assumption: r u P = 1 , r uj = 0 , P ⊆ I u , j ∈ A , A ⊆ I\I u , (5) where P is an observed item-set and A is an unobserved item-set. For the observed item-set P , we define the predicted preference of user u to item-set P in the same way with that of CoFiSet [Pan and Chen, 2013a], i.e., ˆ i ∈P ˆ r u P = � r ui / |P| . For the unobserved item-set A , we define the preference of user u on each item j ∈ A separately. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 11 / 38
Method CoFi-points(i): Likelihood Based on the pointwise preference assumption on item-set, we can have the log-likelihood for a specific user u as follows: 1 ln p (( u , P ) | Θ) r u P [ � |A| . ( 1 − p (( u , j ) | Θ)) 1 − r uj ] (6) j ∈A We use the sigmoid function to approximate the probability, i.e., σ (ˆ r u P ) for p (( u , P ) | Θ) and σ (ˆ r uj ) for p (( u , j ) | Θ)) . We can then rewrite the log-likelihood as: r u P )) + 1 � ln ( σ (ˆ ln ( 1 − σ (ˆ r uj )) . (7) |A| j ∈A Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 12 / 38
Method CoFi-points(i): Objective Function (1/2) Finally, combining all possible observed item-sets and unobserved item-sets of each user u ∈ U , we reach the overall objective function: r u P ))+ 1 � � � � ln ( σ (ˆ ln ( 1 − σ (ˆ r uj )) . (8) |A| u ∈U P⊆I u A⊆I\I u j ∈A Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 13 / 38
Method CoFi-points(i): Objective Function (2/2) Maximizing the overall log-likelihood in Eq.(8) is equal to solve the following optimization problem: � � � min [ f u P + f u A + R (Θ)] , (9) Θ u ∈U P⊆I u A⊆I\I u r u P )) and f u A = − 1 where f u P = − ln ( σ (ˆ � j ∈A ln ( 1 − σ (ˆ r uj )) are loss |A| functions for an observed item-set P and an unobserved item-set A , respectively, and Θ = { U u · , V i · , b u , b i | u ∈ U , i ∈ I} denotes the model parameters to be learned. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 14 / 38
Method Pointwise Preference Assumption on User-set Our assumption: r G ui = 1 , r uj = 0 , u ∈ G , G ⊆ U i , j ∈ A , A ⊆ I\I u , (10) where G is a randomly sampled set of users that have interacted with item i and A is an unobserved item-set. For the observed user-set G , we define the preference of user-set G on item i in the same way with that of GBPR [Pan and Chen, 2013a], i.e., ˆ w ∈G ˆ r G i = � r wi / |G| . We adopt the fused preference of the user-set preference and the individual preference, which combines the effect of user-set into individual preference in the form of ˆ r G ui = p ˆ r G i + ( 1 − p )ˆ r ui . For the unobserved item-set A , we define the preference of user u on each item j ∈ A separately. Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 15 / 38
Method CoFi-points(u): Likelihood The corresponding log-likelihood for a specific user u with a related user-set G and an unobserved item-set A ⊆ I\I u is as follows, 1 ln Prob (( u , G , i ) | Θ) r G ui [ � ( 1 − Prob (( u , j ) | Θ)) 1 − r uj ] |A| . (11) j ∈A Similarly, we use σ (ˆ r G ui ) for Prob (( u , G , i ) | Θ) and σ (ˆ r uj ) for Prob (( u , j ) | Θ)) . We can then rewrite the log-likelihood in Eq.(11) as follows, r G ui )) + 1 � ln ( σ (ˆ ln ( 1 − σ (ˆ r uj )) . (12) |A| j ∈A Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 16 / 38
Method CoFi-points(u): Objective Function (1/2) Finally, combining all possible observed user-set and unobserved item-set of each user u ∈ U , we reach the overall log-likelihood, r G ui ))+ 1 � � � � � ln ( σ (ˆ ln ( 1 − σ (ˆ r uj )) . (13) |A| u ∈U i ∈I u G⊆U i A⊆I\I u j ∈A Li, Pan and Ming (SZU) CoFi-points ACM TIST 2020 17 / 38
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