Recommender systems have become crucial in the modern digital landscape, where personalized content, products, and services are essential for enhancing user experience. This paper explores statistical models for recommender systems, focusing on crossed random effects models and factor analysis. We extend the crossed random effects model to include random slopes, enabling the capture of varying covariate effects among users and items. Additionally, we investigate the use of factor analysis in recommender systems, particularly for settings with incomplete data. The paper also discusses scalable solutions using the Expectation Maximization (EM) and variational EM algorithms for parameter estimation, highlighting the application of these models to predict user-item interactions effectively.

翻译：推荐系统在现代数字环境中已变得至关重要，个性化内容、产品和服务对于提升用户体验至关重要。本文探讨了推荐系统的统计模型，重点关注交叉随机效应模型和因子分析。我们将交叉随机效应模型扩展至包含随机斜率，从而能够捕捉用户和项目间变化的协变量效应。此外，我们研究了因子分析在推荐系统中的应用，特别是在数据不完整场景下的使用。本文还讨论了使用期望最大化（EM）算法和变分EM算法进行参数估计的可扩展解决方案，重点介绍了这些模型在有效预测用户-项目交互中的应用。