Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. Moreover, 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 existing methods, especially when the target matrix is associated with the feature matrix in a nonlinear way.

翻译：多任务学习因多源相关数据驱动的多用途研究而备受关注。此外，基于传导的矩阵补全方法在多标签学习中十分有效。本文提出一种融合特征校准约束的传导矩阵补全算法，其基于多任务学习框架。该算法可同步恢复不完整特征矩阵与目标矩阵。值得注意的是，校准信息能够提升补全效果。具体而言，我们为所提算法提供了统计保障，并研究了校准信息带来的理论改进。同时，该算法具备次线性收敛速率。多组合成数据实验表明，当目标矩阵与特征矩阵存在非线性关联时，本算法表现优于现有其他方法。