  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-$\ell_{1},\ell_{1}$
regularization was proposed in \cite{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-$\ell_{1},\ell_{1}$ regularization and the lack of
adaptivity might result in suboptimal performance. In this paper we propose to
employ an adaptive threshold in the capped-$\ell_{1},\ell_{1}$ 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
\cite{Wang2010}. Empirical studies on both synthetic and real-world data sets
demonstrate the effectiveness of this new variant over the original MSMTFL.
