Online sparse sliced inverse regression for high-dimensional streaming data

Abstract

Due to the demand for tackling the problem of streaming data with high-dimensional covarites, we propose an online sparse sliced inverse regression (OSSIR) method for online sufficient dimension reduction (SDR). The existing online SDR methods focus on the case when [Formula: see text] (dimension of covariates) is small. In this paper, we adapt the sparse sliced inverse regression to cope with high-dimensional streaming data where the dimension [Formula: see text] 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 perform online [Formula: see text] regularization. Theoretical properties of the proposed online learner are established. By comparing with several existing methods in simulations and real data applications, we demonstrate the effectiveness and efficiency of our method.