{"paper":{"title":"Fourier analysis perspective for sufficient dimension reduction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Rustem Takhanov","submitted_at":"2018-08-19T09:41:21Z","abstract_excerpt":"A theory of sufficient dimension reduction (SDR) is developed from an optimizational perspective. In our formulation of the problem, instead of dealing with raw data, we assume that our ground truth includes a mapping ${\\mathbf f}: {\\mathbb R}^n\\rightarrow {\\mathbb R}^m$ and a probability distribution function $p$ over ${\\mathbb R}^n$, both given analytically. We formulate SDR as a problem of finding a function ${\\mathbf g}: {\\mathbb R}^k\\rightarrow {\\mathbb R}^m$ and a matrix $P\\in {\\mathbb R}^{k\\times n}$ such that ${\\mathbb E}_{{\\mathbf x}\\sim p({\\mathbf x})} \\left|{\\mathbf f}({\\mathbf x}) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06191","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"}