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.
翻译:由于需要解决高维共变数据流的问题,我们建议采用在线稀薄的反回归法(OSSIR),以在网上充分减少维度。现有的在线足够维度减少方法侧重于维度小时的情况。在本条中,我们表明,当维度大时,我们的方法可以实现更好的统计准确性和计算速度。我们的方法有两个重要步骤,一个是扩大在线主元分析,以迭接地获得内核矩阵的元值和精子,另一个是使用疏通梯度实现在线的$L ⁇ 1美元规范化。我们还分析了扩展的Candidid-无共变增五氯苯甲醚(CCIPCA)和我们的方法的趋同。通过比较模拟和真实数据应用中的若干现有方法,我们展示了我们方法的实效和效率。