37
4
v1v2 (latest)

Minimization Problems Based on Relative αα-Entropy II: Reverse Projection

Abstract

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted Iα\mathscr{I}_{\alpha}) were studied. Such minimizers were called forward Iα\mathscr{I}_{\alpha}-projections. Here, a complementary class of minimization problems leading to the so-called reverse Iα\mathscr{I}_{\alpha}-projections are studied. Reverse Iα\mathscr{I}_{\alpha}-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (α>1\alpha >1) and in constrained compression settings (α<1\alpha <1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse Iα\mathscr{I}_{\alpha}-projection into a forward Iα\mathscr{I}_{\alpha}-projection. The transformed problem is a simpler quasiconvex minimization subject to linear constraints.

View on arXiv
Comments on this paper