{"paper":{"title":"Density Estimation in Infinite Dimensional Exponential Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aapo Hyv\\\"arinen, Arthur Gretton, Bharath Sriperumbudur, Kenji Fukumizu, Revant Kumar","submitted_at":"2013-12-12T15:09:25Z","abstract_excerpt":"In this paper, we consider an infinite dimensional exponential family, $\\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\\mathbb{R}^d$ can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in $\\mathcal{P}$. The main goal of the paper is to estimate an unknown density, $p_0$ through an element in $\\mathcal{P}$. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3516","kind":"arxiv","version":4},"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"}