{"paper":{"title":"Learning general sparse additive models from point queries in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hemant Tyagi, Jan Vybiral","submitted_at":"2018-01-25T17:38:29Z","abstract_excerpt":"We consider the problem of learning a $d$-variate function $f$ defined on the cube $[-1,1]^d\\subset {\\mathbb R}^d$, where the algorithm is assumed to have black box access to samples of $f$ within this domain. Denote ${\\mathcal S}_r \\subset {[d] \\choose r}; r=1,\\dots,r_0$ to be sets consisting of unknown $r$-wise interactions amongst the coordinate variables. We then focus on the setting where $f$ has an additive structure, i.e., it can be represented as $$f = \\sum_{{\\mathbf j} \\in {\\mathcal S}_1} \\phi_{{\\mathbf j}} + \\sum_{{\\mathbf j} \\in {\\mathcal S}_2} \\phi_{{\\mathbf j}} + \\dots + \\sum_{{\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08499","kind":"arxiv","version":3},"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"}