Transductive Matrix Completion with Calibration for Multi-Task Learning

TL;DR

This paper introduces a transductive matrix completion algorithm with calibration constraints that enhances multi-task learning by simultaneously recovering feature and target matrices, with theoretical guarantees and superior performance on synthetic data.

Contribution

The paper proposes a novel transductive matrix completion method incorporating calibration constraints, improving recovery accuracy and providing theoretical guarantees in multi-task learning.

Findings

Outperforms existing methods on synthetic data

Theoretical guarantee for the algorithm's performance

Calibration improves matrix completion results

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.