Sufficient Dimension Reduction: An Information-Theoretic Viewpoint.
ENTROPY 2022;
24:e24020167. [PMID:
35205462 PMCID:
PMC8871343 DOI:
10.3390/e24020167]
[Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 12/27/2021] [Accepted: 01/18/2022] [Indexed: 11/16/2022]
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.
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