Causal graph, as an effective and powerful tool for causal modeling, is usually assumed as a Directed Acyclic Graph (DAG). However, recommender systems usually involve feedback loops, defined as the cyclic process of recommending items, incorporating user feedback in model updates, and repeating the procedure. As a result, it is important to incorporate loops into the causal graphs to accurately model the dynamic and iterative data generation process for recommender systems. However, feedback loops are not always beneficial since over time they may encourage more and more narrowed content exposure, which if left unattended, may results in echo chambers. As a result, it is important to understand when the recommendations will lead to echo chambers and how to mitigate echo chambers without hurting the recommendation performance. In this paper, we design a causal graph with loops to describe the dynamic process of recommendation. We then take Markov process to analyze the mathematical properties of echo chamber such as the conditions that lead to echo chambers. Inspired by the theoretical analysis, we propose a Dynamic Causal Collaborative Filtering ($\partial$CCF) model, which estimates users' post-intervention preference on items based on back-door adjustment and mitigates echo chamber with counterfactual reasoning. Multiple experiments are conducted on real-world datasets and results show that our framework can mitigate echo chambers better than other state-of-the-art frameworks while achieving comparable recommendation performance with the base recommendation models.

翻译：因果关系图,作为因果关系模型的有效和强有力的工具,通常被假定为“定向循环图 ” 。然而,建议系统通常包含反馈环路,被定义为建议项目的循环过程,将用户反馈纳入模式更新,并重复程序。因此,必须在因果图中纳入环路,准确模拟建议系统动态和迭代数据生成过程。但是,反馈环不总是有益,因为随着时间的推移,它们可能鼓励更多和更多缩小内容的接触,如果不加关注,可能会在回声室中产生结果。因此,建议系统通常包括反馈环路,被定义为建议项目的循环过程,将用户反馈室定义为循环过程,将用户反馈室的减少回声室,而不会损害建议性能。在本文中,我们用因果图来描述建议的动态过程。然后,我们用马尔科夫进程来分析回声室的数学属性,例如通向回声室的条件。在理论分析的启发下,我们提议一个动态的Causal 合作过滤模型,如果留在回声室里,则可能导致回声室。因此,重要的是要了解建议中用户的后端偏向后方位偏好,同时根据可比较的回声室框架进行反向的反向分析。