论文标题
在线稀疏切成薄片的反回归
Online Sparse Sliced Inverse Regression
论文作者
论文摘要
由于需要解决具有高维协变量流数据流的问题，因此我们提出了一种在线稀疏切片逆回归（OSSIR）方法，以减少在线尺寸。现有的在线足够缩小方法集中在尺寸$ p $很小的情况下。在本文中，我们表明，当尺寸$ p $大时，我们的方法可以实现更好的统计准确性和计算速度。我们的方法中有两个重要步骤，一个是将在线主体组件分析扩展到迭代获得内核矩阵的特征值和特征向量，另一个是使用截短的梯度来实现在线$ L_ {1} $正则化。我们还分析了扩展的候选协方差增量PCA（CCIPCA）和我们的方法的收敛性。通过比较模拟和实际数据应用中的几种现有方法，我们证明了我们方法的有效性和效率。
Due to the demand for tackling the problem of streaming data with high dimensional covariates, we propose an online sparse sliced inverse regression (OSSIR) method for online sufficient dimension reduction. The existing online sufficient dimension reduction methods focus on the case when the dimension $p$ is small. In this article, we show that our method can achieve better statistical accuracy and computation speed when the dimension $p$ is large. There are two important steps in our method, one is to extend the online principal component analysis to iteratively obtain the eigenvalues and eigenvectors of the kernel matrix, the other is to use the truncated gradient to achieve online $L_{1}$ regularization. We also analyze the convergence of the extended Candid covariance-free incremental PCA(CCIPCA) and our method. By comparing several existing methods in the simulations and real data applications, we demonstrate the effectiveness and efficiency of our method.
