# DPMF: Decentralized Probabilistic Matrix Factorization for Privacy-Preserving Recommendation
###### Abstract
Although the server in federated learning is only responsible for aggregating and distributing the model, it still has to store a large amount of model information and coordinate communication with various users. This might become a bottleneck when the learning scale becomes large and further lead to single point of failure in practice [10]. Thus, in this study, we focus on implementing a decentralized learning scheme for building a CF model. As shown in Figure 1, by performing local training and exchanging some non-private information with neighbors, users collaboratively learn a global model. In this way, the storage and computing load are transferred to users which improves the scalability and stability of the system. Most CF models cannot learn from both explicit and implicit feedback simultaneously. CF aims to model user preference based on user feedback, which generally has two categories: explicit feedback and implicit feedback [11]. Explicit feedback is often the form of numeric ratings given by users to express the extent to which they like the items. It could measure user preference in a direct and granular way, but some users are reluctant to have such extra operations [12]. In contrast, implicit feedback is easier to be collected. It includes users' behaviors that indirectly reflect their opinion (e.g., browse history, clicking record). However, compared with explicit feedback, it has lower accuracy and granularity. For example, a woman buys a skirt online and finds out she dislikes it after wearing it. Through the above analysis, it is clear that these two forms of feedback are complementary  
Figure 1: The comparison between centralized learning, federated learning, and decentralized learning. to each other since explicit feedback is higher in quality while implicit feedback is higher in quantity. As far as we know, few CF models are based both on explicit and implicit feedback. Thus, in this study we devise a matrix co-factorization model to cope with the heterogeneity between these two forms of feedback. Our contributions. In this study, we first explore a probabilistic model specifically suitable for handling both explicit and implicit feedback and then devise a decentralized method called DPMF to protect users' sensitive information. To the best of our knowledge, this is the first privacy-preserving framework for recommendation with both explicit and implicit feedback. The main contributions are listed as follows. * We devise a novel probabilistic matrix factorization method for recommender systems. It uses both explicit and implicit feedback simultaneously to model user preferences and item characteristics, which is practical and interpretable in rating prediction and item recommendation. * We propose a novel decomposing strategy to decompose the shared information among users into two parts, and only share the non-private part. In this way, the model not only gains a guarantee of convergence by exchanging the public information, but also maintains user privacy as the private information is kept locally by users. * We propose a secure and efficient method to train our model. By finding neighbors from the trust statement, users exchange public model information with others. The public and personal model gradients are updated through stochastic gradient descent. Extensive experiments on two real-world datasets show that our method outperforms the existing state-of-the-art CF methods with lower RMSE loss in rating prediction task and higher precision in item recommendation task. The rest of this study is organized as follows. We introduce the background in Section 2 and then discuss the preliminaries and the system model in Section 3. We conduct experiment and discuss the model performance in Section 4. Finally, we conclude this study in Section 5.