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Minimization Problems Based on Relative $alpha$-Entropy II: Reverse Projection

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 نشر من قبل M. Ashok Kumar
 تاريخ النشر 2014
  مجال البحث الهندسة المعلوماتية
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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.



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