Recently latent factor model (LFM) has been drawing much attention in recommender systems due to its good performance and scalability. However, existing LFMs predict missing values in a user-item rating matrix only based on the known ones, and thus the sparsity of the rating matrix always limits their performance. Meanwhile, semi-supervised learning (SSL) provides an effective way to alleviate the label (i.e., rating) sparsity problem by performing label propagation, which is mainly based on the smoothness insight on affinity graphs. However, graph-based SSL suffers serious scalability and graph unreliable problems when directly being applied to do recommendation. In this paper, we propose a novel probabilistic chain graph model (CGM) to marry SSL with LFM. The proposed CGM is a combination of Bayesian network and Markov random field. The Bayesian network is used to model the rating generation and regression procedures, and the Markov random field is used to model the confidence-aware smoothness constraint between the generated ratings. Experimental results show that our proposed CGM significantly outperforms the state-of-the-art approaches in terms of four evaluation metrics, and with a larger performance margin when data sparsity increases.Latent factor model. Among the existing recommendation approaches, latent factor model (LFM) has been drawing much attention due to its good performance and scalability. LFM uses a low dimensional user and item latent factors to represent the characteristics of each user and each item, and uses the product of them to represent the user's rating on the item. LFM has drawn much attention recently due to its good performance and scalability [1,4,19,24,26,28,34,35,37,43,44,47]. As users have actions (e.g., rate and buy) on some items, LFM aims to predict the users' unknown actions on other items. The tendency of a user's action on an item can be indicated by a real-valued number, i.e., rating or label. Thus, the recommendation problem is also known as the unknown ratings prediction problem [41]. In practice, however, many LFMs have to evaluate very large user and item sets, where the user-item (U-I) matrix is extremely sparse-such data sparsity has always been its main challenge [42]. Semi-supervised learning. SSL uses unlabeled data to either modify or reprioritize hypotheses obtained from labeled data alone, and thus can alleviate the label sparsity problem by adopting the graph information between data [40]. Towards effective SSL, affinity graph-based smoothness approaches have attracted much research interests, which follow the smoothness insight: close nodes on an affinity graph have similar labels. Graph-based SSL is appealing recently because it is easy to implement and gives rise to closed-form solutions [9,13,16,45,46,52]. However, graph-based SSL directly predicts the unknown ratings in the original U-I matrix, and thus suffers from the scalability problem.As a key insight of this paper, we identify the marriage of SSL and LFM. The main insights of SSL (i.e., smoothness...