A convex formulation for learning a shared predictive structure from multiple tasks.
A convex formulation for learning a shared predictive structure from multiple tasks.
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DOI：
10.1109/tpami.2012.189
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发表时间：
2013-05
影响因子：
23.6
通讯作者：
Ye J
中科院分区：
文献类型：
--
作者：
Chen J;Tang L;Liu J;Ye J
在本文中，我们考虑从多个相关的任务，以提高泛化性能，通过提取其共享结构的学习问题。交替结构优化（阿索）算法，它耦合所有的任务使用一个共享的特征表示，已成功地应用于各种多任务学习问题。然而，阿索是非凸的，交替算法只能找到一个局部解。首先，我们提出了一个改进的阿索制定（iASO）的多任务学习的基础上，一个新的正则化。然后，我们将iASO，一个非凸的配方，到一个放松的凸（rASO）。有趣的是，我们的理论分析表明，rASO在一定条件下找到了其非凸对应物iASO的全局最优解。rASO可以等效地重新表述为半定规划（SDP），然而，其不可扩展到大型数据集。我们建议分别采用块坐标下降（BCD）方法和加速投影梯度（APG）算法来找到rASO的全局最优解，我们还开发了有效的算法来解决BCD和APG中涉及的关键子问题。在Yahoo网页数据集和果蝇基因表达模式图像数据集上的实验验证了算法的有效性和效率，验证了理论分析的正确性。
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.