Consistency of trace norm minimization
Consistency of trace norm minimization
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DOI：
10.5555/1390681.1390716
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发表时间：
2007-10
期刊：
影响因子：
--
通讯作者：
F. Bach
中科院分区：
文献类型：
--
作者：
F. Bach
通过奇异值之和进行正则化（也称为迹范数）是一种用于估计低阶矩形矩阵的流行技术。在本文中，我们扩展了Lasso的一些一致性结果，为迹范数最小化与平方损失的秩一致性提供充要条件。我们还提供了一个自适应版本，即使不满足非自适应版本的必要条件，该版本也能保持排名一致。
Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss. We also provide an adaptive version that is rank consistent even when the necessary condition for the non adaptive version is not fulfilled.