Transfer to Rank for Top-N Recommendation Wei Dai, Qing Zhang, Weike Pan ∗ and Zhong Ming ∗ daiwei20171@email.szu.edu.cn, qingzhang1992@qq.com, panweike@szu.edu.cn, mingz@szu.edu.cn National Engineering Laboratory for Big Data System Computing Technology and College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 1 / 27
Introduction Problem Definition Top-N Recommendation Input: Ratings in the form of (user, item, rating) triples. Goal: Recommend a personalized ranked list of items to each user u from the items that user u has not examined or rated before, i.e., I\I u , where I u = I E u denotes the set of examined or rated items by user u . Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 2 / 27
Introduction Challenge How to exploit users’ explicit feedback more sufficiently? Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 3 / 27
Introduction Overall of Our Solution Coarse-to-Fine Transfer to Rank (CoFiToR) We view the rating records from three different but related 1 perspectives, i.e., examinations , scores and purchases . We decompose a user’s shopping process into three stages, i.e., 2 E-stage , S-stage and P-stage , which correspond to three specific questions, including (i) whether an item will be examined by a user , (ii) how an item will be scored by a user , and (iii) whether an item will finally be purchased by a user . Our CoFiToR progressively models users’ preferences from a coarse granularity to a fine granularity by transferring knowledge in the form of candidate item lists. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 4 / 27
Introduction Advantages of Our Solution It is able to model and simulate a user’s shopping process in a 1 coarse-to-fine manner. It is a generic, flexible and efficient transfer learning framework for 2 top-N recommendation. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 5 / 27
Introduction Notations Table: Mathematical notations and explanations. Symbol Descriptions n number of users m number of items d dimension of latent feature vector U = { u } user set I = { i } item set R = { ( u , i , r ui ) } rating records in training data rating of user u to item i r ui ¯ r ui normalized rating of user u to item i I P items purchased by u in training data u I E items examined by u in training data u ˆ r ui predicted preference of user u to item i U u · ∈ R 1 × d user u ’s latent feature vector V i · ∈ R 1 × d item i ’s latent feature vector b u ∈ R user u ’s bias b i ∈ R item i ’s bias Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 6 / 27
Background Bayesian Personalized Ranking The loss function of BPR can be formulated as follows, � � � min − ln σ (ˆ r ui − ˆ r uj ) , (1) Θ u ∈U i ∈I P j ∈I\I P u u r ui = U u · V T where ˆ i · + b i is the prediction rule, U u · is user u ’s latent vector, V i · is item i ’s latent vector, and b i is the bias of item i . BPR orders items by modeling the distance between the preference on a purchased item and an un-purchased item, i.e., ˆ r ui − ˆ r uj , via a pairwise loss function. Due to its excellence in effectiveness and efficiency, we choose BPR as an essential component in our three-staged recommendation framework to ensure that the candidate items are what the users are likely to examine. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 7 / 27
Background Probabilistic Matrix Factorization The loss function of PMF can be formulated as follows, r ui ) 2 , � min ( r ui − ˆ (2) Θ ( u , i , r ui ) ∈R r ui = U u · V T where ˆ i · + b u + b i + µ is the prediction rule, U u · is user u ’s latent vector, V i · is item i ’s latent vector, b u is the bias of user u , b i is the bias of item i , and µ is the global average. PMF is a popular pointwise regression-oriented recommendation method that models a user’s preference as the inner product of two low-rank user and item feature vectors, and it scales well to large and sparse datasets. In our proposed solution, the goal of adopting PMF is to refine the candidate list of items from a complementary view of rating scores. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 8 / 27
Background Transfer to Rank (1/2) In the first stage, the general objective of global preference learning is 1 as follows, Prob( E ∪ E R | Θ g ) , (3) where E is the examination behavior, E R denotes the (user, item) pairs of the rating records, and Θ g is the set of model parameters used to govern the generation of the combined examination behavior E ∪ E R . In the second stage, ToR focuses on users’ local preference learning 2 aiming at refining the candidate list of items L g generated from the first stage. The general objective of local preference learning is as follows, Prob( R| Θ ℓ ; L g ) , (4) where Θ ℓ is the set of model parameters used to govern the generation of the rating behavior R . Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 9 / 27
Background Transfer to Rank (2/2) The two sequential stages of ToR aim to answer the following two related questions: Whether a user will examine an item; How will a user like an item if he/she has examined it. Hence, ToR can simulate a user’s shopping process to some extent. But for different users, even he/she assigns a high score to an item, it doesn’t mean that the user will finally purchase the item and vice versa. That is to say, users not only differ in tastes of items, but also in purchase choices, which is decisive but neglected by ToR. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 10 / 27
Method CoFiToR: Assumptions If a user examines an item, it means that the user is interested in the 1 item; A user virtually or implicitly scores an item if and only if he/she has 2 examined it; If a user likes an item, there is a high probability that he/she will 3 purchase it; A user may not purchase the item even if he/she likes it and vice 4 versa. Based on these four assumptions, we design a three-staged transfer learning framework to bridge the connection among the three aforementioned actions in a proper way. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 11 / 27
Method CoFiToR: Illustration Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 12 / 27
Method CoFiToR: Objective Function The optimization problem is as follows, Prob( E , S , P|R ) , (5) where E , S and P denote the derived examinations , scores and purchases from the original rating records. We decompose it into three sequential sub-problems resulting in our three-staged solution, Prob( E| Θ E ) → Prob( S| Θ S ; L E ) → Prob( P| Θ P ; L S ) , (6) where Θ E , Θ S and Θ P are the model parameters to be learned, and L E and L S are the candidate lists of likely to be examined items and high-score items, respectively. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 13 / 27
Method E-stage: Whether Will It Be Examined Adopted model : Revised BPR Goal : Extract items that users are most likely to examine Input : Examinations E = { ( u , i ) | ( u , i , r ui ) ∈ R} Output : Candidate list L E with N E items of each user The objective function is as follows, � � � min ¯ f uij , (7) r ui Θ u ∈U i ∈I E j ∈I\I E u u r ui = (2 r ui − 1) / 2 5 is a normalized version of the rating r ui of user u where ¯ to item i in the original rating records R , and I E u is the set of items examined by u in training data. Notice that the rating ¯ r ui is expected to widen the gap between positive items and negative items, and distinguish positive items with different rating values. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 14 / 27
Method S-stage: How Will It Be Scored Adopted model : PMF Goal : Model users’ score preferences Input : Scores S = R , candidate list L E Output : Candidate list L S with N S items of each user ( N S < N E ) Notice that the objective function is the same as that in PMF. We bridge two types of user actions, i.e., examinations and scores, based on the aforementioned assumption, i.e., a user virtually or implicitly scores an item if and only if he/she has examined it. Notice that in ToR, the obtained candidate list L S in this stage will be used for recommendation immediately without a further refinement, which is one major difference between the two-staged solution ToR and our three-staged framework CoFiToR. Dai, Zhang, Pan and Ming (SZU) Coarse-to-Fine Transfer to Rank (CoFiToR) IEEE Trans. on Big Data 15 / 27
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