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In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted $mathscr{I}_{alpha}$) were studied. Such minimizers were called forward $mathscr{I}_{alpha}$-projections. Here, a complementary class of minimization problems leading to the so-called reverse $mathscr{I}_{alpha}$-projections are studied. Reverse $mathscr{I}_{alpha}$-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems ($alpha >1$) and in constrained compression settings ($alpha <1$). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse $mathscr{I}_{alpha}$-projection into a forward $mathscr{I}_{alpha}$-projection. The transformed problem is a simpler quasiconvex minimization subject to linear constraints.
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $alpha$-entropies (denoted $mathscr{I}_{alpha}$), arise as redundancies under mismatched comp
This paper studies forward and reverse projections for the R{e}nyi divergence of order $alpha in (0, infty)$ on $alpha$-convex sets. The forward projection on such a set is motivated by some works of Tsallis {em et al.} in statistical physics, and th
New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verd{u} for general probability measures. A second bound improves the tightness of an inequality by Csisz{a}r and T
The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their i
We study minimization of a parametric family of relative entropies, termed relative $alpha$-entropies (denoted $mathscr{I}_{alpha}(P,Q)$). These arise as redundancies under mismatched compression when cumulants of compressed lengths are considered in