# User Trust Inference in Online Social Networks: A Message Passing Perspective
## 3 The Proposed Model
### Prerequisites  
A variety of studies and literature [6; 21; 37; 38] have found that trust has many unique features and characteristics, and they are embedded in user profiles and other UGC data in OSNs. Based on relevant findings of trust and OSNs, we give some key principles and assumptions on which our proposed model stands in this section, without formal proofs. **Assumption 1**. : _Through activities of users in online social networks, user-generated content, such as reviews, posts, votes, issued trust, and so on, represent and bear the user's attitude, credibility, and trustworthiness._  
A survey [37] suggests that numerous factors, including logical trust attributes (e.g., experience, frequency, stability, and rationality), emotional trust attributes (e.g., hope, fear, and regret) and relational trust attributes (e.g., similarity), contribute to construct individual trust through social capital and social activities. Meanwhile, in online social networks, the above factors are expressed through various types of user-generated contents and user activities. Therefore, trust can be harvested through a variety of UGC data that exists in OSNs, such as their posted reviews or articles, cast ratings and votes, and issued trust relationships. **Assumption 2**. : _For a trust relationship between a trustor and a trustee, not only the trustee but also the trustor contributes to the relationship formation._  
The formation of a trust relationship involves the trustor who evaluates and issues trust, and the trustee who presents and receives it, which makes trust asymmetric and subjective. The issuance of a trust relationship is determined by the trustor through their perception of the trustee's trustworthiness and how others perceive it. However, due to the difficulty of modeling trust's subjectivity, many studies only focus on making use of UGC data that represent trustees' credibility [39; 40; 41], leaving trust an objective concept and measure. Based on this point, we bear the mind in this paper that although same types of user data are being used for collecting trust information, they could serve different purposes for the trustor and the trustee involved in a trust relationship. For example, the same characteristics extracted from one of a user's reviews may serve as different features: the type of attitude features that suggest how the user trusts others, or the type of trustworthiness features which indicate how he is being trusted by others. **Assumption 3**. : _Users bearing similarities in their profiles or activities have a higher likelihood to establish trust relationships._  
That is suggested by the homophily effect, which is one of the most important theories that attempt to explain why people establish trust relations with each other [42]. For example, in the situation of product reviewing, people with similar tastes about items are more likely to trust each other. Taking the previous two assumptions into consideration, we could further state that a group of similar users may build trust relationships with similar users from another group, if there exists a trust relationship between a pair of users from each group. This also implies trust's incomplete transitivity property. **Assumption 4**. : _In datasets from online social networks, no observable or explicit trust relationship between two users does not truly guarantee there will not be any trust between them._  
For example, we may infer a trust relationship issued by [PERSON] to [PERSON], provided that (1) there are many other users who have certain similar characteristics as [PERSON] has, and they also trust [PERSON], or (2) [PERSON] trusts many other users who have traits in common with [PERSON]. However, it is worth noting that there are quite a few reasons that the relationship of [PERSON] and [PERSON] is not present in the network. It can be explained from three perspectives:  
* Due to some particular or unknown facts, [PERSON] does not trust [PERSON]; the trust relationship does not exist, and therefore, it will never be observed.