Online Sparse Sliced Inverse Regression

TL;DR

This paper introduces an online sparse sliced inverse regression method designed for high-dimensional streaming data, improving statistical accuracy and computational efficiency over existing methods.

Contribution

It extends online PCA with eigenvector estimation and uses truncated gradient for online L1 regularization, suitable for large-dimensional data.

Findings

Outperforms existing methods in accuracy and speed

Effective in high-dimensional streaming data scenarios

Validated through simulations and real data applications

Abstract

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.