## 1 Introduction  
In the current era of exponential growth in internet information, the volume of available data has increased geometrically. As users search for information, it has become challenging to efficiently and accurately access desired content. Personalized recommendation algorithms [1] leverage user behavioral data to assist users in rapidly obtaining relevant content amidst data overload [2]. Presently, personalized recommendation algorithms can be broadly categorized into three types: content-based recommendation algorithms, collaborative filtering recommendation algorithms, and hybrid recommendation algorithms. Among these, collaborative filtering recommendation algorithms, as the most widely applied recommendation technique, primarily focus on prediction and recommendation. Collaborative filtering recommendation algorithms can be further divided into item-based collaborative filtering recommendation algorithms and user-based collaborative filtering recommendation algorithms. In the item-based approach, similar items are identified and tagged, and recommendations are made to users based on items similar to those they prefer. The user-based collaborative filtering recommendation algorithm operates by recommending based on groups of similar users [3]. Leveraging historical user behavioral data features, it groups users with high similarity into clusters, enabling prediction of ratings [4]. With the rapid expansion of the user base, traditional user-based collaborative filtering recommendation algorithms have encountered challenges such as data sparsity and suboptimal feature extraction, which hinder the ability to thoroughly and comprehensively uncover user interests [5]. As a result, scholars both domestically and internationally have begun conducting research to address these issues. [PERSON] et al. [6] were among the first to propose a recommendation algorithm based on deep learning models. They employed a restricted Boltzmann machine model to characterize rating data. [PERSON] et al. [7] introduced a recommendation algorithm based on deep belief networks and Probabilistic Matrix Factorization, combining learned latent features with collaborative filtering and applying them to music recommendation. [PERSON] et al. [8] introduced a recommendation algorithm based on deep variational matrix factorization, utilizing deep nonlinear structures to independently capture latent features of both users and items. [PERSON] et al. [9] devised a matrix factorization algorithm based on Bernoulli distribution, leveraging the binary nature of model distribution to enhance recommendation accuracy and reliability. [PERSON] et al. [10] proposed a joint matrix factorization algorithm based on transfer learning, which could improve the effectiveness of similarity measurement by mining latent features of users. [PERSON] et al. [11] introduced a biased deep matrix factorization model that employed neural networks to enhance matrix factorization. [PERSON] et al. [12] put forth a regularized least squares optimization algorithm with case-weighting, leading to improved collaborative filtering recommendation performance. While the aforementioned recommendation algorithms have to some extent alleviated the issues of data sparsity and suboptimal feature extraction, they primarily analyze the associations between users and items based solely on user behavior information, without considering auxiliary item information [13; 14; 15]. Consequently, they may fall short of fully capturing users' genuine preferences. To address this limitation, this paper introduces a recommendation algorithm based on an improved Conditional Variational Autoencoder (CVAE) and Constrained Probabilistic Matrix Factorization (CPMF). Firstly, enhancements are made to the CVAE by adding latent layers and introducing random noise to these layers, thereby constraining the data features. This augmentation improves the model's robustness against interference and enhances its generative capabilities.