论文标题
$ \ ell_1 $ -norm约束多块稀疏规范相关分析通过近端下降
$\ell_1$-norm constrained multi-block sparse canonical correlation analysis via proximal gradient descent
论文作者
论文摘要
多块CCA构建线性关系，解释了多个数据块的相干变化。我们将多块CCA问题视为找到领先的广义特征向量，并提议通过具有$ \ ell_1 $约束的高维数据来通过近端梯度下降算法解决。特别是，我们使用对近端迭代的约束的衰减序列，并表明所得估计值在适当的假设下是最佳的速率。尽管以前的几项工作已经使用迭代方法证明了$ \ ell_0 $约束问题的最佳性，但仍然缺乏对$ \ ell_1 $约束配方的理论理解水平。我们还描述了一个易于实现的通缩程序，以顺序估计多个特征向量。我们将我们的建议与几种现有方法进行了比较，这些方法在R cran上可用，并且所提出的方法在模拟和真实数据示例中都显示出竞争性的性能。
Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient descent algorithm with $\ell_1$ constraint for high dimensional data. In particular, we use a decaying sequence of constraints over proximal iterations, and show that the resulting estimate is rate-optimal under suitable assumptions. Although several previous works have demonstrated such optimality for the $\ell_0$ constrained problem using iterative approaches, the same level of theoretical understanding for the $\ell_1$ constrained formulation is still lacking. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially. We compare our proposals to several existing methods whose implementations are available on R CRAN, and the proposed methods show competitive performances in both simulations and a real data example.
