Transductive Matrix Completion with Calibration for Multi-Task Learning

Hengfang Wang; Yasi Zhang; Xiaojun Mao; Zhonglei Wang

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arXiv · 2302.09834

Transductive Matrix Completion with Calibration for Multi-Task Learning

Hengfang Wang·Yasi Zhang·Xiaojun Mao·Zhonglei Wang

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Abstract

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.

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BibTeX RIS

Hengfang Wang, Yasi Zhang, Xiaojun Mao, Zhonglei Wang. 2023-02-20. Transductive Matrix Completion with Calibration for Multi-Task Learning. https://arxiv.org/abs/2302.09834

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