# FMGAN: A Filter-Enhanced MLP Debias Recommendation Model Based on Generative Adversarial Network
## 2 Related Work
### Generative Adversarial Network and GAN-Based Recommendation  
[PERSON] proposed a novel approach called Generative Adversarial Network (GAN) [28], which was initially applied in image generation and achieved significant success [29]. The GAN architecture comprises a generator G, a discriminator D, and adversarial learning between them. G generates fake data by learning real data, and its objective is to produce synthetic data that is as close as possible to real data. D distinguishes between real and fake data and aims to accurately differentiate the two. The adversarial learning process of G and D in GAN can be viewed as a max-min game, where [PERSON] continually generates more accurate data through learning to reduce the probability of D identifying real data, while D continuously learns to increase the difference between real and fake data, improving its ability to distinguish between them. After adversarial learning, [PERSON] can learn to capture the ideal distribution of users and generate credible recommendation results that differ from real data. GAN has not only been successful in image generation but has also found applications in other domains, such as WaveGAN [30] for music generation and SeqGAN [31] for sentence generation. IRGAN [32] is an information retrieval system that combines recommendation systems, web search, question answering systems, and GAN. In the domain of recommendation systems, IRGAN employs GAN architecture where the generator G aims to produce item IDs that match the user's preferences, and the discriminator D estimates the probability of an item ID originating from real interaction data or being generated by [PERSON] The IRGAN method has successfully applied the GAN framework to the recommender system field, and its effectiveness has led to further developments. One such development is the CFGAN [33; 34] model, which employs a vector training method instead of the pointwise [35] training method used in IRGAN. Vector data have several inherent advantages, such as richer and more complete user features and their compatibility with neural network input patterns. Additionally, updating network parameters with stochastic gradient descent is feasible with vector data. In CFGAN, the user interaction vector \(\mathbf{r_{u}}\) and random noise vector \(\mathbf{c_{u}}\) are used as inputs to the generator, which directly generates the user interaction vector \(\mathbf{\hat{r}_{u}}\), represented as an n-dimensional sparse vector. Unlike IRGAN, D evaluates the given vector as the user's history interaction vector \(\mathbf{r_{u}}\), rather than calculating the probability that G generates the interaction vector \(\mathbf{\hat{r}_{u}}\). While the original GAN model is primarily applied to dense data, the data in the recommendation system are often sparse due to data collection issues. CFGAN utilizes binary implicit feedback vectors, where 1 denotes user interaction with the item, and 0 denotes no interaction. However, this type of bias data may cause G to generate an unhelpful output consisting of all 1s. To address the bias issue, CFGAN proposes three solutions, including zero-reconstruction (ZR), partial-masking (PM), and a combination of both methods (ZP). The ZR method integrates the G-generated list with real interactions for MSE loss calculation, mitigating overfitting. The PM method incorporates negative sampling into each user's training process. Specifically, a mask vector \(\mathbf{k_{u}}\) is formed by randomly selecting a certain number of items, and an n-dimensional indicator vector \(\mathbf{e_{u}}\) is generated to represent user u's interaction with item i. By adding \(\mathbf{e_{u}}\) and \(\mathbf{k_{u}}\) and multiplying the resulting vector elementwise with the user's historical interaction data, a new interaction vector is generated, achieving the desired sampling effect. Negative sampling enables the model to learn more diverse user preferences, thereby improving its ability to analyze the optimal state and overcome exposure bias.