# DPMF: Decentralized Probabilistic Matrix Factorization for Privacy-Preserving Recommendation
###### Abstract  
Collaborative filtering is a popular approach for building an efficient and scalable recommender system. However, it has not unleashed its full potential due to the following problems. (1) Serious privacy concerns: collaborative filtering relies on aggregated user data to make personalized predictions, which means that the centralized server can access and compromise user privacy. (2) Expensive resources required: conventional collaborative filtering techniques require a server with powerful computing capacity and large storage space, so that the server can train and maintain the model. (3) Considering only one form of user feedback: most existing works aim to model user preferences based on explicit feedback (e.g., ratings) or implicit feedback (e.g., purchase history, viewing history) due to their heterogeneous representation; however, these two forms of feedback are abundant in most collaborative filtering applications, can both affect the model, and very few works studied the simultaneous use thereof. To solve the above problems, in this study we focus on implementing decentralized probabilistic matrix factorization for privacy-preserving recommendations. First, we explore the existing collaborative filtering algorithms and propose a probabilistic matrix co-factorization model. By integrating explicit and implicit feedback into a shared probabilistic model, the model can cope with the heterogeneity between these two forms of feedback. Further, we devise a decentralized learning method that allows users to keep their private data on the end devices. A novel decomposing strategy is proposed for users to exchange only non-private information, in which stochastic gradient descent is used for updating the models. Complexity analysis proves that our method is highly efficient with linear computation and communication complexity. Experiments conducted on two real-world datasets _FilmTrust_ and _Epinions_ show that our model gains a guarantee of convergence as the RMSE decreases quickly within 100 rounds of iterations. Compared with the state-of-the-art models, our model achieves lower model loss in rating prediction task and higher precision in item recommendation task. p 2022 2022 2022 2022 2022  
mation is exposed to the service provider. Thus, some data privacy regulations, such as General Data Protection Regulation (GDPR) [3], have been published. These regulations attempt to place restrictions on the collection, storage, and use of user data. To tackle this privacy problem, federated learning (FL) [4] is proposed to legally and efficiently make use of users' data. FL distributes the model learning process to users' end devices, making it possible to train a global model from user-specific local models, which ensures that user's private data never leaves their end devices. However, CF under federated learning still has privacy issues as it is susceptible to some attacks. For example, [PERSON] et al. [5] prove the practicality in conducting backdoor attacks in federated learning. [PERSON] et al. [6] study and evaluate poisoning attack in federated learning system based on generative adversarial nets (GAN). Recently, decentralized learning (DL) [7] has drawn people's attention in many real-world applications. As shown in Figure 1, in decentralized learning the model is learned collaboratively by a group of users without needing a centralized server. However, malicious participants might steal privacy from other users in the communication phase [8]. Thus, we propose a decomposing strategy in our decentralized scheme to ensure that users exchanging only non-private information with each other, which shows practicality in preserving user privacy. (2) Conventional CF models might be limited by high resource requirements. Except for privacy concerns, [PERSON] et al. [9] point out that in order to maintain the user data and train the CF model, centralized learning needs a server with high storage and computing capacity.