Minimization Problems Based on Relative $α$-Entropy II: Reverse Projection
Year: 2014
Type: preprint
Abstract: In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted $\mathscr{I}_α$) were studied. Such minimizers were called forward $\mathscr{I}_α$-projections. Here, a complementary class of minimization problems leading to the so-called reverse $\mathscr{I}_α$-projections are studied. Reverse $\mathscr{I}_α$-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems ($α>1$) and in constrained compression settings ($α<1$). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse $\mathscr{I}_α$-projection into a forward $\mathscr{I}_α$-projection. The transformed problem is a simpler quasiconvex minimization subject to linear constraints.
Source: arXiv (Cornell University)
Authors: Kumar, M. Ashok, Sundaresan, Rajesh
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4299845660