Multi-stage Multi-task feature learning via adaptive threshold
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Multi-task feature learning aims to identity the shared features among tasks to improve generalization. It has been shown that by minimizing non-convex learning models, a better solution than the convex alternatives can be obtained. Therefore, a non-convex model based on the capped-ℓ_1,ℓ_1 regularization was proposed in Gong2013, and a corresponding efficient multi-stage multi-task feature learning algorithm (MSMTFL) was presented. However, this algorithm harnesses a prescribed fixed threshold in the definition of the capped-ℓ_1,ℓ_1 regularization and the lack of adaptivity might result in suboptimal performance. In this paper we propose to employ an adaptive threshold in the capped-ℓ_1,ℓ_1 regularized formulation, where the corresponding variant of MSMTFL will incorporate an additional component to adaptively determine the threshold value. This variant is expected to achieve a better feature selection performance over the original MSMTFL algorithm. In particular, the embedded adaptive threshold component comes from our previously proposed iterative support detection (ISD) method Wang2010. Empirical studies on both synthetic and real-world data sets demonstrate the effectiveness of this new variant over the original MSMTFL.
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