Sufficient Dimension Reduction: An Information-Theoretic Viewpoint |
| |
Authors: | Debashis Ghosh |
| |
Affiliation: | Department of Biostatistics and Informatics, Colorado School of Public Health, Aurora, CO 80045, USA; |
| |
Abstract: | 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. |
| |
Keywords: | central subspace information bottleneck single-index model |
|
|