Sufficient Dimension Reduction: An Information-Theoretic Viewpoint

There has been a lot of interest in sufficient dimension reduction (SDR) methodologies, as well as nonlinear extensions in the statistics literature. The SDR methodology has previously been motivated by several considerations: (a) finding data-driven subspaces that capture the essential facets of regression relationships; (b) analyzing data in a 'model-free' manner. In this article, we develop an approach to interpreting SDR techniques using information theory. Such a framework leads to a more assumption-lean understanding of what SDR methods do and also allows for some connections to results in the information theory literature.

Automated summary

In this article, an approach to interpreting SDR techniques using information theory is developed, leading to a less assumption-lean understanding of what SDR methods do and allowing for connections to results in the information theory literature.