Personalized Recommendation with Implicit Feedback via Learning - PowerPoint PPT Presentation

Personalized Recommendation with Implicit Feedback via Learning Pairwise Preferences over Item-sets Weike Pan 1 , 2 , Li Chen 2 ∗ and Zhong Ming 1 ∗ panweike@szu.edu.cn, lichen@comp.hkbu.edu.hk, mingz@szu.edu.cn 1 College of Computer Science and Software Engineering Shenzhen University, Shenzhen, China 2 Department of Computer Science Hong Kong Baptist University, Hong Kong, China This work is an extension of our previous work [Pan and Chen, 2013]. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 1 / 34

Introduction Problem Definition Personalized Recommendation with Implicit Feedback Input: Observed feedback R tr = { ( u , i ) } from n users and m items. Goal: Generate a personalized ranking list of items for each user u from the whole set of unobserved items I tr \I tr u . Notice that this problem is also called one-class collaborative filtering (OCCF) or collaborative filtering with implicit feedback. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 2 / 34

Introduction Challenges/Limitations For pointwise preference on an item: Finding a good weighting strategy for each observed feedback is a very difficult task in real applications, since we usually have implicit feedback only. Treating all observed feedback as “like” and unobserved feedback as “dislike” may mislead the learning process. For pairwise preferences over two items: The pairwise assumption may not hold for each item pair. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 3 / 34

Introduction Overall of Our Solution Pairwise preferences over item-sets : a new and relaxed assumption that a user is likely to prefer a set of observed items to a set of unobserved items. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 4 / 34

Introduction Advantage of Our Solution Pairwise preferences over item-sets is likely to be more accurate and the corresponding pairwise relationship is more likely to be valid. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 5 / 34

Introduction Notations (1/2) Notation Description n number of users m number of items U tr = { u } n training set of users u = 1 U tr training set of users w.r.t. item i i U te ⊆ U tr test set of users I tr = { i } m training set of items i = 1 I tr training set of items w.r.t. user u u I te test set of items w.r.t. user u u P ⊆ I tr set of items ( presence of observation) u A ⊆ I tr \I tr set of items ( absence of observation) u Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 6 / 34

Introduction Notations (2/2) u ∈ U tr user index i , j ∈ I tr item index R tr = { ( u , i ) } training data R te = { ( u , i ) } test data ˆ r ui preference of user u on item i ˆ r uj preference of user u on item j ˆ r u P preference of user u on item-set P ˆ r u A preference of user u on item-set A ˆ r uij , ˆ r ui A , ˆ r u PA , ˆ r u P j pairwise preferences of user u Θ set of model parameters 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 Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 7 / 34

Method Preference Assumption on Item-sets (1/2) A user u ’s preference on an item-set (a set of items) is defined as a function of user u ’s preferences on items in the item-set. For example, a user u ’s preference on an item-set P can be ˆ i ∈P ˆ r u P = � r ui / |P| , or in other forms. A user u ’s pairwise preferences over two item-sets is defined as the difference between user u ’s preferences on two item-sets. For example, a user u ’s pairwise preferences over item-sets P and A can be ˆ r u PA = ˆ r u P − ˆ r u A , or ˆ r u PA = ˆ r u P − ˆ r uj , j ∈ A , or in other forms. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 8 / 34

Method Preference Assumption on Item-sets (2/2) With the aforementioned two definitions, we further relax the assumption of pairwise preferences over items as made in [Rendle et al., 2009] and propose a new assumption called pairwise preferences over item-sets , represented in the following four forms, ˆ r u P > ˆ Set vs. Set (SS) : r u A , (1) ˆ r ui > ˆ Many “One vs. One” (MOO) : r uj , i ∈ P , j ∈ A , (2) ˆ r ui > ˆ Many “One vs. Set” (MOS) : r u A , i ∈ P , (3) ˆ r u P > ˆ Many “Set vs. One” (MSO) : r uj , j ∈ A , (4) Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 9 / 34

Method Optimization Problems Assuming that a user u is likely to prefer an item-set P to an item-set A , we may introduce the aforementioned constraints in Eqs.(1-4). For a pair of item-sets P and A , we can have the following optimization problems, R ( u , P , A ) , s.t. ˆ r u P > ˆ SS : min r u A , (5) Θ u R ( u , P , A ) , s.t. ˆ r ui > ˆ MOO : min r uj , i ∈ P , j ∈ A , (6) Θ u R ( u , P , A ) , s.t. ˆ r ui > ˆ MOS : min r u A , i ∈ P , (7) Θ u R ( u , P , A ) , s.t. ˆ r u P > ˆ MSO : min r uj , j ∈ A , (8) Θ u where ˆ r ui = b i + U u · V T i · is the predicted preference of user u on item i , Θ u = { U u · , V i · , b i , i ∈ I tr } , and R ( u , P , A ) is an L 2 regularization term used to avoid overfitting during parameter learning [Koren, 2010]. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 10 / 34

Method Objective Functions (1/2) We relax the constraints in Eqs.(1-4) and introduce a loss function in the objective function, min L ( u , P , A ) + R ( u , P , A ) , (9) Θ u where L ( u , P , A ) is the loss function w.r.t. user u ’s preferences on item-sets P and A . For each user u , we have the following optimization problem, � � min L ( u , P , A ) + R ( u , P , A ) , (10) Θ u P⊆I tr A⊆I tr \I tr u u where P is a subset of items randomly sampled from I tr u that denotes a set of items with observed feedback from user u , and A is a subset of items randomly sampled from I tr \I tr u that denotes a set of items without observed feedback from user u . Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 11 / 34

Method Objective Functions (2/2) Finally, we put all users together and reach the following optimization problem, � � � min L ( u , P , A ) + R ( u , P , A ) , (11) Θ u ∈U tr P⊆I tr A⊆I tr \I tr u u where Θ = { U u · , V i · , b i , u ∈ U tr , i ∈ I tr } denotes the parameters to be learned. The loss function L ( u , P , A ) is defined on the user u ’s pairwise preferences over item-sets. The regularization term R ( u , L , A ) = 2 � U u · � 2 + � 2 � V i · � 2 + β v 2 � V j · � 2 + β v α u i ∈P [ α v j ∈A [ α v 2 � b i � 2 ] + � 2 � b j � 2 ] is used to avoid overfitting during parameter learning [Koren, 2010], where α u , α v , β v are hyper-parameters. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 12 / 34

Method Loss Function In order to directly compare our pairwise preferences over item-sets assumption with pairwise preferences over items as made in BPRMF [Rendle et al., 2009], we study four specific loss functions, L ( u , P , A ) = − ln σ (ˆ SS : r u PA ) , (12) L ( u , P , A ) = − 1 1 � � ln σ (ˆ MOO : r uij ) , (13) |P| |A| i ∈P j ∈A L ( u , P , A ) = − 1 � ln σ (ˆ MOS : r ui A ) , (14) |P| i ∈P L ( u , P , A ) = − 1 � ln σ (ˆ MSO : r u P j ) , (15) |A| j ∈A where ˆ r u PA = ˆ r u P − ˆ r u A , ˆ r uij = ˆ r ui − ˆ r uj , ˆ r uiA = ˆ r ui − ˆ r uA , ˆ r u P j = ˆ r u P − ˆ r uj , 1 ˆ i ∈P ˆ r ui / |P| , ˆ j ∈A ˆ r u P = � r u A = � r uj / |A| , and σ ( x ) = 1 + exp ( − x ) is the sigmoid function. Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 13 / 34

Method The Gradients in CoFiSet(SS) For each ( u , P , A ) triple, we have ∂ L ( u , P , A ) ( ¯ V P· − ¯ ∇ U u · = V A· ) + α u U u · , (16) ∂ ˆ r u PA ∂ L ( u , P , A ) U u · ∇ V i · = |P| + α v V i · , i ∈ P , (17) ∂ ˆ r u PA ∂ L ( u , P , A ) − U u · ∇ V j · = |A| + α v V j · , j ∈ A , (18) ∂ ˆ r u PA ∂ L ( u , P , A ) 1 ∇ b i = |P| + β v b i , i ∈ P , (19) ∂ ˆ r u PA ∂ L ( u , P , A ) − 1 ∇ b j = |A| + β v b j , j ∈ A , (20) ∂ ˆ r u PA where ∂ L ( u , P , A ) = ∂ − ln σ (ˆ r u PA ) r u PA ) , ¯ = − σ ( − ˆ V P· = � i ∈P V j · / |P| , and ∂ ˆ ∂ ˆ r u PA r u PA ¯ V A· = � j ∈A V j · / |A| . Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 14 / 34

Method The Gradients in CoFiSet(MOO) For each ( u , P , A ) triple, we have ∂ L ( u , P , A ) � � ∇ U u · = ( V i · − V j · ) + α u U u · , (21) ∂ ˆ r uij i ∈P j ∈A ∂ L ( u , P , A ) � ∇ V i · = U u · + α v V i · , i ∈ P , (22) ∂ ˆ r uij j ∈A ∂ L ( u , P , A ) � ∇ V j · = ( − U u · ) + α v V j · , j ∈ A , (23) ∂ ˆ r uij i ∈P ∂ L ( u , P , A ) � ∇ b i = 1 + β v b i , i ∈ P , (24) ∂ ˆ r uij j ∈A ∂ L ( u , P , A ) � ∇ b j = ( − 1 ) + β v b j , j ∈ A , (25) ∂ ˆ r uij i ∈P where ∂ L ( u , P , A ) = − 1 1 |A| σ ( − ˆ r uij ) . ∂ ˆ |P| r uij Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 15 / 34