# User Trust Inference in Online Social Networks: A Message Passing Perspective
## 1 Introduction  
Trust exists in many different forms in various disciplines. For instance, the trust on the World Wide Web can be trust in content, trust in services, and trust in people [1]. Although different disciplines take different definitions and forms of trust, they commonly aim to solve the problem of accurately evaluating trust between two entities, to help complex systems make informed decisions. For example, some peer-to-peer system may take advantage of trust to curb malicious attacks and maintain network robustness [2]. A complex model selection system could evaluate the trustworthiness of a cloud-based machine learning model-as-a-service (MaaS) for industrial Internet of Things and smart city services [3]. Some online social service could use trust to improve the quality of recommendations [4]. Some researchers leveraged a trust network to study the relational antecedents of members' influence in organizations [5]. Without loss of generality, we focus on user trust in online social networks (OSNs) in this paper, which is one of the most common types of trust. We followed [6] to define user trust in OSNs: a subjective expectation an OSN user has about another user's future behavior. Social trust is a basic social construct [7], and it enables people to collectively liveand work in groups. In social networks, trust helps people find whom to trust, to build beneficial or even reciprocal social relationships, so that the quality of interindividual interactions could be improved and the risks of social activities reduced. Many online social services embrace trust management systems to help their users to build and expand their webs of trust so that users can keep being engaged in their services [8]. For example, Twitter has deployed a user recommendation service called \"Who to Follow\" to use a user's \"circle of trust\" for recommending new connections to the user [9]. Being a key contributing factor in many complex systems, trust has been elaborately explored and researched, and it has been proven to be helpful in securing social commerce [10], recommending trustworthy users [11], providing accurate and personalized recommendations [4; 12; 13; 14], filtering trustworthy authorities or users [15], finding opinion leaders or trolls [16], maximizing influence diffusion [17], and decision making [18; 19; 20]. However, data of trust information, such as trust relationships, do not always explicitly or abundantly exist for the above-mentioned tasks to use. Therefore, the study of trust inference is necessary and practical for social network analysis and relevant decision making tasks. The process of inferring an unknown trust relationship in OSNs, which is often referred to as trust inference, involves exploitation of social construct elements. The sources of relevant trust information that assembles social constructs in OSNs include but are not limited to existing trust relationships and data created by the users involved in the relationships, such as their activities, including posting reviews and casting votes, and other content generated by them (user-generated contents, UGC). Various algorithms and models have been proposed to infer trust in OSNs [21]. Some of them make use of topological data, i.e., the web of trust relationships or the trust network, to predict trust relationships. However, due to the ever-present issue that observable trust relationships in OSNs are often sparse, some vanilla algorithms for predicting trust are prevented from achieving more accurate predicted results in large real OSNs. With the aim of tackling the issue, other methods use both the web of trust and UGC data to achieve more accurate results in inferring trust. Nevertheless, there are three major problems holding back existing trust inference models. Firstly, if additional UGC data are available, some of them and various types of interplay among them are discarded when the trust inference framework integrates them with the trust network, making the model prone to generating less accurate results.