The field of data imputation and recommendation systems is rapidly evolving, with a focus on addressing issues related to missing data, privacy concerns, and fairness. Recent developments have led to the creation of novel models and algorithms that incorporate techniques such as nonlinear PID control, federated learning, and causal convolutional low-rank representation. These advancements aim to improve the accuracy and efficiency of data imputation and recommendation systems, while also ensuring the protection of user data and promoting fairness. Notable papers in this area include those that propose innovative solutions to mitigate information loss during aggregation, preserve personalized local features, and balance individual fairness with provider fairness. Some of the key techniques being explored include the use of particle swarm optimization, regret-aware re-ranking, and double-norm aggregated tensor latent factorization. Overall, the field is moving towards the development of more sophisticated and robust models that can effectively handle complex data sets and real-world applications. Noteworthy papers include: Latent Tensor Factorization with Nonlinear PID Control for Missing Data Recovery, which proposes a novel NPIL model that outperforms state-of-the-art models in convergence rate and accuracy. FedCIA: Federated Collaborative Information Aggregation for Privacy-Preserving Recommendation, which introduces a new aggregation paradigm that mitigates information loss and preserves personalized local features.