{"paper":{"title":"Minimization Problems Based on Relative $\\alpha$-Entropy II: Reverse Projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"M. Ashok Kumar, Rajesh Sundaresan","submitted_at":"2014-10-21T06:40:28Z","abstract_excerpt":"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 pow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5550","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}