Asymmetric Bayesian Personalized Ranking for One-Class Collaborative - PowerPoint PPT Presentation

Asymmetric Bayesian Personalized Ranking for One-Class Collaborative Filtering Shan Ouyang, Lin Li, Weike Pan ∗ and Zhong Ming ∗ { ouyangshan, lilin20171 } @email.szu.edu.cn, { panweike, mingz } @szu.edu.cn College of Computer Science and Software Engineering Shenzhen University, Shenzhen, China Ouyang et al. (SZU) ABPR RecSys 2019 1 / 24

Introduction Problem Definition One-Class Collaborative Filtering Input: A set of (user, item) pairs R = { ( u , i ) } , where each ( u , i ) pair means that user u has a positive feedback to item i . Goal: recommend each user u ∈ U a personalized ranked list of items from the set of unobserved items, i.e., I\I u . Ouyang et al. (SZU) ABPR RecSys 2019 2 / 24

Introduction Horizontal Pairwise Preference Assumption A user prefers an interacted item to an un-interacted item, e.g., user 3 prefers item 2 to item 4, i.e., ( 3 , 2 ) ≻ ( 3 , 4 ) or ˆ r 32 > ˆ r 34 . In general, we have, ˆ r ui > ˆ r uj , i ∈ I u , j ∈ I\I u . Bayesian personalized ranking (BPR) [Rendle et al., 2009] is built on this assumption. Ouyang et al. (SZU) ABPR RecSys 2019 3 / 24

Introduction Vertical Pairwise Preference Assumption An item is preferred by an interacted user to an un-interacted user, e.g., item 2 is preferred by user 3 to user 6, i.e., ( 3 , 2 ) ≻ ( 6 , 2 ) or ˆ r 32 > ˆ r 62 . In general, we have, ˆ r ui > ˆ r wi , u ∈ U i , w ∈ U\U i . We call a model built on this transposed preference assumption BPR T . Ouyang et al. (SZU) ABPR RecSys 2019 4 / 24

Introduction Mutual Pairwise Preference Assumption Combining those two types of pairwise preference assumptions, we have, ˆ r ui > ˆ r uj , ˆ r ui > ˆ r wi , i ∈ I u , j ∈ I\I u , u ∈ U i , w ∈ U\U i . Mutual Bayesian personalized ranking (MBPR) [Yu et al., 2016] is built on this symmetric assumption. Ouyang et al. (SZU) ABPR RecSys 2019 5 / 24

Introduction Our Asymmetric Assumption The symmetric mutual pairwise preference assumption may not hold, in particular of the vertical one, because different users may have different evaluation standards, which will then make the preferences of different users uncomparable. We propose an asymmetric pairwise preference assumption A user prefers an interacted item to an un-interacted item. An item is preferred by a group of interacted users to a group of un-interacted users. Ouyang et al. (SZU) ABPR RecSys 2019 6 / 24

Introduction Overall of Our Solution We propose a novel and improved preference assumption, i.e., 1 asymmetric pairwise preference assumption, where we relax the vertical preference assumption to make it more reasonable and comparable. With the proposed first asymmetric assumption for OCCF, we then 2 design a novel recommendation algorithm called asymmetric Bayesian personalized ranking (ABPR). Ouyang et al. (SZU) ABPR RecSys 2019 7 / 24

Introduction Notations Table: Notations and descriptions. Notation Description n number of users m number of items u , w user ID i , j item ID r ui preference of user u to item i U = { u } the whole set of users I = { i } the whole set of items R = { ( u , i ) } one-class feedback U i a set of users who interact with item i I u a set of items interacted by user u P a group of users who interact with an item N a group of users who do not interact with an item ˆ r ui predicted preference of user u to item i d number of latent dimensions U u · ∈ R 1 × d user u ’s latent feature vector V i · ∈ R 1 × d item i ’s latent feature vector b i ∈ R item i ’s bias Ouyang et al. (SZU) ABPR RecSys 2019 8 / 24

Method Asymmetric Pairwise Preference Assumption (1/2) We keep the horizontal pairwise preference assumption in BPR [Rendle et al., 2009] and assume that an item is preferred by a group of interacted users to a group of un-interacted users in order to make the vertical one more reasonable and comparable, ˆ r ui > ˆ r uj , ˆ r P i > ˆ r N i , (1) where i ∈ I u , j ∈ I\I u , P ⊆ U i , N ⊆ U\U i and u ∈ P . Ouyang et al. (SZU) ABPR RecSys 2019 9 / 24

Method Asymmetric Pairwise Preference Assumption (2/2) For instantiation of the relationship between the group preferences ˆ r P i and ˆ r N i , we propose “Many ‘Group vs. One’ (MGO)” inspired by “Many ‘Set vs. One’ (MSO)” [Pan et al., 2019], ˆ r P i > ˆ r wi , w ∈ N , (2) 1 where ˆ u ′ ∈P ˆ r P i = � r u ′ i is the overall preference of user-group P to |P| item i . r u ′ i = U u ′ · V T Notice that ˆ i · + b u ′ + b i is the prediction rule for the preference of user u ′ to item i , where U u ′ · ∈ R 1 × d and V i · ∈ R 1 × d are latent feature vectors of user u ′ and item i , respectively, and b u ′ ∈ R and b i ∈ R are the bias of user u ′ and item i , respectively. Ouyang et al. (SZU) ABPR RecSys 2019 10 / 24

Method Asymmetric Bayesian Personalized Ranking (ABPR) Based on the asymmetric pairwise preference assumption in Eqs.(1-2), we reach an objective function in our asymmetric Bayesian personalized ranking (ABPR) for each quintuple ( u , i , j , P , N ) , 1 � Θ − ln σ (ˆ ln σ (ˆ min r uij ) − r i P w ) + reg ( u , i , j , P , N ) , (3) |N| w ∈N where Θ = { U u · , V i · , b u , b i , u ∈ U , i ∈ I} are the model parameters to be learned, ˆ r uij = ˆ r ui − ˆ r uj and ˆ r i P w = ˆ r P i − ˆ r wi denote the corresponding preference differences, and 2 || V i · || 2 + α 2 || V j · || 2 + α 2 || b i || 2 + α 2 || b j || 2 + reg ( u , i , j , P , N ) = α 2 || U u ′ · || 2 + α 2 || U w · || 2 + α 2 || b u ′ || 2 ] + � 2 || b w || 2 ] is the � u ′ ∈P [ α w ∈N [ α regularization term used to avoid overfitting. Ouyang et al. (SZU) ABPR RecSys 2019 11 / 24

Method Gradients We then have the gradients of the model parameters w.r.t. the tentative objective function in Eq.(3), 1 r i P w ) V i · � ∇ U u · = − σ ( − ˆ r uij )( V i · − V j · ) − |N| σ ( − ˆ |P| + α U u · , w ∈N 1 r i P w ) V i · |P| + α U u ′ · , u ′ ∈ P\{ u } , � |N| σ ( − ˆ ∇ U u ′ · = − w ∈N ∇ U w · = − 1 |N| σ ( − ˆ r i P w )( − V i · ) + α U w · , w ∈ N , 1 U u · � � ∇ V i · = − σ ( − ˆ r uij ) U u · − |N| σ ( − ˆ r i P w )( |P| − U w · ) + α V i · , w ∈N u ∈P ∇ V j · = − σ ( − ˆ r uij )( − U u · ) + α V j · , ∇ b i = − σ ( − ˆ r uij ) + α b i , ∇ b j = − σ ( − ˆ r uij )( − 1 ) + α b j , 1 r i P w ) 1 � |N| σ ( − ˆ ∇ b u = − |P| + α b u , u ∈ P , w ∈N ∇ b w = − 1 |N| σ ( − ˆ r i P w )( − 1 ) + α b w , w ∈ N . Ouyang et al. (SZU) ABPR RecSys 2019 12 / 24

Method Algorithm 1: for t = 1 , 2 , .., T do for t 2 = 1 , 2 , .., |R| do 2: Randomly pick a (user, item) pair ( u , i ) from R . 3: Randomly pick an item j from I\I u . 4: Randomly pick |P| − 1 users from U i \{ u } . 5: Randomly pick |N| users from U\U i . 6: Calculate the gradients w.r.t. the tentative objection 7: function in Eq.(3). Update the corresponding model parameters, i.e., 8: U u · , U w · , V i · , V j · , b i , b j , b u , and b w , where u ∈ P and w ∈ N . end for 9: 10: end for Ouyang et al. (SZU) ABPR RecSys 2019 13 / 24

Experiments Datasets Table: Statistics of the first copy of each dataset used in the experiments. Notice that n is the number of users and m is the number of items, and |R| , |R va | and |R te | denote the numbers of (user, item) pairs in training data, validation data and test data, respectively. |R va | |R te | Dataset n m |R| ML20M 138,493 27,278 5,997,245 1,999,288 1,998,877 NF50KU 50,000 17,770 3,551,369 1,183,805 1,183,466 Ouyang et al. (SZU) ABPR RecSys 2019 14 / 24

Experiments Evaluation Metrics We adopt five ranking-oriented metrics [Chen and Karger, 2006, Manning et al., 2008, Valcarce et al., 2018] to evaluate the performance: Precision@5 Recall@5 F1@5 NDCG@5 1-call@5 Ouyang et al. (SZU) ABPR RecSys 2019 15 / 24

Experiments Baselines In order to study the effectiveness of our proposed asymmetric pairwise preference assumption and the corresponding recommendation algorithm ABPR directly, we include the following closely related baseline methods, including (i) basic matrix factorization with square loss (MF), (ii) matrix factorization with logistic loss (LogMF) [Johnson, 2014], (iii) factored item similarity model (FISM) [Kabbur et al., 2013], (iv) Bayesian personalized ranking (BPR) [Rendle et al., 2009], (v) BPR with transposed pairwise preference assumption (BPR T ), and (vi) mutual BPR (MBPR) [Yu et al., 2016]. Notice that MF, LogMF and FISM are based on the pointwise preference assumption, and BPR, BPR T and MBPR are based on the pairwise preference assumptions. Ouyang et al. (SZU) ABPR RecSys 2019 16 / 24