The emergence of big data has enabled the creation of significant models by allowing the storage of large data volumes. Transfer learning is a machine learning technique that transfers knowledge between different domains by utilizing pretrained models from the source domain to optimize the target domain. In contrast, inductive matrix completion is a method that leverages side information from multiple sources to improve task performance. This paper explores inductive matrix completion within the transfer learning framework, with our proposed approach assuming group sparsity for the difference between the core matrices of the target and source domains. Theoretical guarantees of our method are investigated to demonstrate the gains achieved through transfer learning compared with standard inductive matrix completion. Several synthetic experiments are conducted to evaluate the performance of the proposed approach and existing methods, demonstrating that our method outperforms others.

Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. More- over, transduction with matrix completion is a useful method in multi-label learning. In this paper, we propose a transductive matrix completion algorithm that incorporates a calibration constraint for the features under the multi-task learning framework. The proposed algorithm recovers the incomplete feature matrix and target matrix simultaneously. Fortunately, the calibration information improves the completion results. In particular, we provide a statistical guarantee for the proposed algorithm, and the theoretical improvement induced by calibration information is also studied. Moreover, the proposed algorithm enjoys a sub-linear convergence rate. Several synthetic data experiments are conducted, which show the proposed algorithm out-performs other methods, especially when the target matrix is associated with the feature matrix in a nonlinear way.