Multi-Stage Multi-Task Feature Learning
This work addresses a bottleneck in multi-task sparse feature learning for applications like computer vision and biomedical informatics, offering an incremental improvement over existing convex methods.
The paper tackles the suboptimality of convex sparse regularization in multi-task feature learning by proposing a non-convex formulation and MSMTFL algorithm, achieving a better parameter estimation error bound and demonstrating effectiveness on synthetic and real-world datasets compared to state-of-the-art methods.
Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multi-task sparse feature learning algorithms are formulated as a convex sparse regularization problem, which is usually suboptimal, due to its looseness for approximating an $\ell_0$-type regularizer. In this paper, we propose a non-convex formulation for multi-task sparse feature learning based on a novel non-convex regularizer. To solve the non-convex optimization problem, we propose a Multi-Stage Multi-Task Feature Learning (MSMTFL) algorithm; we also provide intuitive interpretations, detailed convergence and reproducibility analysis for the proposed algorithm. Moreover, we present a detailed theoretical analysis showing that MSMTFL achieves a better parameter estimation error bound than the convex formulation. Empirical studies on both synthetic and real-world data sets demonstrate the effectiveness of MSMTFL in comparison with the state of the art multi-task sparse feature learning algorithms.