## 2 Related Work  
The issue of fairness in recommender systems has garnered increasing attention, leading researchers to focus on addressing selection bias. Various methods have been proposed to eliminate selection bias, such as inverse propensity scoring, meta-learning, homogeneous data, and causal diagrams. These approaches aim to mitigate the impact of selection bias and promote fair recommendations. [PERSON] et al. [12] introduced a novel approach that utilized two causal graphs to depict the generation process of biased and unbiased feedback within recommender systems. Their model incorporated the learning of biased embedding vectors, which consisted of independent biased and unbiased components, thus imposing constraints on the learning process. The presence of selection bias gives rise to issues of non-random missing data. [PERSON] et al. [13] introduced the concepts of item observability and user selection to elucidate the generation of non-random missing scores. They proposed the tripartite collaborative filtering (TCF) framework to jointly model the three key aspects of score generation: item observability, user selection, and scoring. This framework aims to estimate non-random missing scores by employing the matrix decomposition method. Subsequently, the TCF framework is transformed into a tripartite probabilistic matrix factorization (TPMF) model, which effectively mitigates the limitations associated with estimating non-random missing scores. In addition, [PERSON] et al. [14] incorporated non-random missing assumptions into the domain of social recommendation and presented the SPMF-MNAR algorithm. This algorithm captures the scoring data acquisition process by considering user preferences and social influence, thereby enhancing the performance of social recommendation algorithms. [PERSON] et al. [15] also introduced a meta-learning approach to address the challenges associated with propensity estimation model selection and high variance. Their method is based on an asymmetric three-training model framework, wherein two trainers generate data with reliable scores and a separate predictor performs the final prediction. This approach significantly mitigates the limitations of the propensity score model. The propensity score method is a reliable approach to mitigate selection bias, allowing for unbiased recommendations by assigning weights to each data point based on the reciprocal of the propensity score. [PERSON] et al. [11] introduced an inverse propensity score estimation method for learning recommender systems in the presence of selection bias. They derived a matrix factorization approach that effectively eliminates selection bias, offering a conceptually simple and highly scalable solution. However, the performance of propensity score-based recommendation systems is often influenced by the choice of the propensity estimation model and the issue of high variance. To address the high variance problem associated with propensity estimation models, [PERSON] et al. [16] proposed a dual-robust estimator for ground truth ranking. This estimator enhances the variance and error bounds of existing unbiased estimators, ensuring unbiased ranking measurements for ground truth. Similarly, [PERSON] et al. [17] introduced a doubly robust estimator (DR) that combines estimation error and propensity in a doubly robust manner. This approach yields unbiased performance estimates and mitigates the impact of propensity variance. Furthermore, [PERSON] et al. [18] conducted a study on the bias and variance of the double robust estimator. Building upon existing estimators, they proposed a more robust estimator called more robust doubly robust (MRDR). This enhanced estimator further reduces variance while maintaining dual robustness. The aforementioned related studies primarily rely on estimating the propensity score using the marginal probability of a user's rating for an item, which possesses certain limitations.