RT Journal Article
JF IEEE Transactions on Pattern Analysis & Machine Intelligence
YR 2013
VO 35
SP 1025
TI A Convex Formulation for Learning a Shared Predictive Structure from Multiple Tasks
A1 Jun Liu,
A1 Jieping Ye,
A1 Jianhui Chen,
A1 Lei Tang,
K1 Optimization
K1 Algorithm design and analysis
K1 Vectors
K1 Fasteners
K1 Complexity theory
K1 Prediction algorithms
K1 Acceleration
K1 accelerated projected gradient
K1 Multitask learning
K1 shared predictive structure
K1 alternating structure optimization
AB In this paper, we consider the problem of learning from multiple related tasks for improved generalization performance by extracting their shared structures. The alternating structure optimization (ASO) algorithm, which couples all tasks using a shared feature representation, has been successfully applied in various multitask learning problems. However, ASO is nonconvex and the alternating algorithm only finds a local solution. We first present an improved ASO formulation (iASO) for multitask learning based on a new regularizer. We then convert iASO, a nonconvex formulation, into a relaxed convex one (rASO). Interestingly, our theoretical analysis reveals that rASO finds a globally optimal solution to its nonconvex counterpart iASO under certain conditions. rASO can be equivalently reformulated as a semidefinite program (SDP), which is, however, not scalable to large datasets. We propose to employ the block coordinate descent (BCD) method and the accelerated projected gradient (APG) algorithm separately to find the globally optimal solution to rASO; we also develop efficient algorithms for solving the key subproblems involved in BCD and APG. The experiments on the Yahoo webpages datasets and the Drosophila gene expression pattern images datasets demonstrate the effectiveness and efficiency of the proposed algorithms and confirm our theoretical analysis.
PB IEEE Computer Society, [URL:http://www.computer.org]
SN 0162-8828
LA English
DO 10.1109/TPAMI.2012.189
LK http://doi.ieeecomputersociety.org/10.1109/TPAMI.2012.189