Social Relations Model for Collaborative Filtering Wu-Jun Lif and Dit-Yan Yeung t Shanghai Key Laboratory of Scalable Computing and Systems Department of Computer Science and Engineering,Shanghai Jiao Tong University,China Department of Computer Science and Engineering Hong Kong University of Science and Technology,Hong Kong,China liwujunecs.situ.edu.cn,dyyeungecse.ust.hk Abstract models(Koren 2008),are the most representative model- based methods.MF methods can make use of either proba- We propose a novel probabilistic model for collaborative fil- bilistic (Lim and Teh 2007:Salakhutdinov and Mnih 2008b) tering (CF),called SRMCoFi,which seamlessly integrates both linear and bilinear random effects into a principled or non-probabilistic (Srebro,Rennie,and Jaakkola 2004; framework.The formulation of SRMCoFi is supported by Rennie and Srebro 2005:Takacs et al.2008)formulations. both social psychological experiments and statistical theo- Recently,some hybrid models combining both memory- ries.Not only can many existing CF methods be seen as spe- based and model-based techniques have also emerged(Ko- cial cases of SRMCoFi,but it also integrates their advan- ren2008). tages while simultaneously overcoming their disadvantages The solid theoretical foundation of SRMCoFi is further sup- ported by promising empirical results obtained in extensive Social Relations Model The social relations model! experiments using real CF data sets on movie ratings (SRM)(Kenny 1994;Li and Loken 2002)has been widely used for modeling dyadic data appeared in many fields,in- cluding social psychology,behavioral science and statisti- Introduction cal science.2 SRM was first introduced in the context of in- Collaborative Filtering Collaborative filtering (CF) terpersonal perception studying the beliefs that people have (Breese,Heckerman,and Kadie 1998)does not exploit about others.During the perception process,there exist a explicit user profiles but only past activities of the users, perceiver (or called actor)and a target (or called partner). such as their transaction history or product satisfaction For example,Bob might have beliefs that his friend,Mary. expressed in ratings,to predict the future activities of the is intelligent.Here,Bob corresponds to a perceiver and Mary users.In a typical CF task,we often use a sparse matrix R to a target. of size N x M to denote the rating or preference values on To collect dyadic data,there are two basic designs:round- the items given by the users.Here N denotes the number of robin design and block design.In the round-robin design, users,M is the number of items,and each matrix element each person interacts with or rates every other person in a Rij represents the preference of item j given by user i.The group.In the block design,a group is divided into two sub- matrix A is sparse because many elements are missing,and groups and members from each subgroup interact or rate the such elements Rij are assigned the value of 0 to indicate members of the other subgroup.Sometimes only half of the that item j has not been rated by user i.The goal of CF is data are gathered from the block design,which is referred to learn a function to predict some of the missing elements to as a half-block design.More specifically,in a half-block in R based on the observed elements. design,a group is divided into two subgroups(say A and Existing CF methods can be divided into two main cate- B),and only the members from one subgroup (say A)rate gories (Sarwar et al.2001;Koren 2008;Zhen,Li,and Yeung the members of the other subgroup (say B),but not vice 2009):memory-based and model-based methods.Memory- versa.As stated in (Kenny 1994,page 24),a half-block de- based methods predict new ratings by (weighted)averaging sign is typical when the targets are presented on videotapes the ratings of similar users or items.According to whether or movies.Hence,the CF problem can be seen as an exam- similarity is defined based on users or items,memory- ple of the half-block design in the perception study because based methods can be further divided into user-based meth- only users rate items but not the other way around. ods (Breese,Heckerman,and Kadie 1998)and item-based However,it should be noted that SRM cannot be directly methods(Sarwar et al.2001).Unlike memory-based meth- applied to the CF problem because the focus of SRM is on ods,model-based methods learn a model from data using the analysis of variance (ANOVA)over actors,partners as statistical learning techniques.Methods based on matrix fac- well as the relationships between actors and partners.For torization (MF)(Takacs et al.2008),or called latent factor http://davidakenny.net/srm/soremo.htm Copyright C)2011,Association for the Advancement of Artificial 2http://davidakenny.net/doc/srmbiblio.pdf Intelligence (www.aaai.org).All rights reserved. lists hundreds of references on various applications of SRM.Social Relations Model for Collaborative Filtering Wu-Jun Li† and Dit-Yan Yeung‡ † Shanghai Key Laboratory of Scalable Computing and Systems Department of Computer Science and Engineering, Shanghai Jiao Tong University, China ‡ Department of Computer Science and Engineering Hong Kong University of Science and Technology, Hong Kong, China liwujun@cs.sjtu.edu.cn, dyyeung@cse.ust.hk Abstract We propose a novel probabilistic model for collaborative fil￾tering (CF), called SRMCoFi, which seamlessly integrates both linear and bilinear random effects into a principled framework. The formulation of SRMCoFi is supported by both social psychological experiments and statistical theo￾ries. Not only can many existing CF methods be seen as spe￾cial cases of SRMCoFi, but it also integrates their advan￾tages while simultaneously overcoming their disadvantages. The solid theoretical foundation of SRMCoFi is further sup￾ported by promising empirical results obtained in extensive experiments using real CF data sets on movie ratings. Introduction Collaborative Filtering Collaborative filtering (CF) (Breese, Heckerman, and Kadie 1998) does not exploit explicit user profiles but only past activities of the users, such as their transaction history or product satisfaction expressed in ratings, to predict the future activities of the users. In a typical CF task, we often use a sparse matrix R of size N × M to denote the rating or preference values on the items given by the users. Here N denotes the number of users, M is the number of items, and each matrix element Rij represents the preference of item j given by user i. The matrix R is sparse because many elements are missing, and such elements Rij are assigned the value of 0 to indicate that item j has not been rated by user i. The goal of CF is to learn a function to predict some of the missing elements in R based on the observed elements. Existing CF methods can be divided into two main cate￾gories (Sarwar et al. 2001; Koren 2008; Zhen, Li, and Yeung 2009): memory-based and model-based methods. Memory￾based methods predict new ratings by (weighted) averaging the ratings of similar users or items. According to whether similarity is defined based on users or items, memory￾based methods can be further divided into user-based meth￾ods (Breese, Heckerman, and Kadie 1998) and item-based methods (Sarwar et al. 2001). Unlike memory-based meth￾ods, model-based methods learn a model from data using statistical learning techniques. Methods based on matrix fac￾torization (MF) (Takacs et al. 2008), or called latent factor ´ Copyright c 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. models (Koren 2008), are the most representative model￾based methods. MF methods can make use of either proba￾bilistic (Lim and Teh 2007; Salakhutdinov and Mnih 2008b) or non-probabilistic (Srebro, Rennie, and Jaakkola 2004; Rennie and Srebro 2005; Takacs et al. 2008) formulations. ´ Recently, some hybrid models combining both memory￾based and model-based techniques have also emerged (Ko￾ren 2008). Social Relations Model The social relations model1 (SRM) (Kenny 1994; Li and Loken 2002) has been widely used for modeling dyadic data appeared in many fields, in￾cluding social psychology, behavioral science and statisti￾cal science.2 SRM was first introduced in the context of in￾terpersonal perception studying the beliefs that people have about others. During the perception process, there exist a perceiver (or called actor) and a target (or called partner). For example, Bob might have beliefs that his friend, Mary, is intelligent. Here, Bob corresponds to a perceiver and Mary to a target. To collect dyadic data, there are two basic designs: round￾robin design and block design. In the round-robin design, each person interacts with or rates every other person in a group. In the block design, a group is divided into two sub￾groups and members from each subgroup interact or rate the members of the other subgroup. Sometimes only half of the data are gathered from the block design, which is referred to as a half-block design. More specifically, in a half-block design, a group is divided into two subgroups (say A and B), and only the members from one subgroup (say A) rate the members of the other subgroup (say B), but not vice versa. As stated in (Kenny 1994, page 24), a half-block de￾sign is typical when the targets are presented on videotapes or movies. Hence, the CF problem can be seen as an exam￾ple of the half-block design in the perception study because only users rate items but not the other way around. However, it should be noted that SRM cannot be directly applied to the CF problem because the focus of SRM is on the analysis of variance (ANOVA) over actors, partners as well as the relationships between actors and partners. For 1http://davidakenny.net/srm/soremo.htm 2http://davidakenny.net/doc/srmbiblio.pdf lists hundreds of references on various applications of SRM