Abstract: We consider the problem of data feature selection prior to inference task specification, which is central to high-dimensional learning. Introducing natural notions of universality for such problems, we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and practically useful learning methodology. The development reveals the key roles of the singular value decomposition, Hirschfeld-Gebelein-Renyi maximal correlation, canonical correlation and principle component analyses, Tishby's information bottleneck, Wyner's common information, Ky Fan…