{"paper":{"title":"Minimum HGR Correlation Principle: From Marginals to Joint Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"David Tse, Farzan Farnia, Meisam Razaviyayn, Sreeram Kannan","submitted_at":"2015-04-22T23:39:56Z","abstract_excerpt":"Given low order moment information over the random variables $\\mathbf{X} = (X_1,X_2,\\ldots,X_p)$ and $Y$, what distribution minimizes the Hirschfeld-Gebelein-R\\'{e}nyi (HGR) maximal correlation coefficient between $\\mathbf{X}$ and $Y$, while remains faithful to the given moments? The answer to this question is important especially in order to fit models over $(\\mathbf{X},Y)$ with minimum dependence among the random variables $\\mathbf{X}$ and $Y$. In this paper, we investigate this question first in the continuous setting by showing that the jointly Gaussian distribution achieves the minimum HG"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06010","kind":"arxiv","version":1},"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"}