Sliced Inverse Regression for datastreams: An introduction

In this tutorial, we focus on data arriving sequentially by block in a stream. A semiparametric regression model involving a common EDR (Effective Dimension Reduction) direction β is assumed in each block. Our goal is to estimate this direction at each arrival of a new block. A simple direct approach consists of pooling all the observed blocks and estimating the EDR direction by the SIR (Sliced Inverse Regression) method. But in practice, some disadvantages become apparent such as the storage of the blocks and the running time for high dimensional data. To overcome these drawbacks, we propose an adaptive SIR estimator of β. The proposed approach is faster both in terms of computational complexity and running time, and provides data storage benefits. A graphical tool is provided in order to detect changes in the underlying model such as a drift in the EDR direction or aberrant blocks in the data stream. This is a joint work with Marie Chavent, Vanessa Kuentz-Simonet, Benoit Liquet, Thi Mong Ngoc Nguyen and Jerome Saracco.