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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.08499","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-25T17:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"d8b59c254107edf026c9a828e6936f0c66b87384180bd389ec46fc39a9a487a0","abstract_canon_sha256":"33d8d4a48fce9136a57a4e7880c519765d2c8b9d69914cb3a4cf7adf3b156e66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:16.104987Z","signature_b64":"nbDFt1bKuIjMAtrnvzJM2bSff12vQXe0U9BXituH2DO3DHyccWLfu8SUkpAbtSar2hCCL6WfncU5s57HUdoMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efbcb44db53339f917fed0de4af0dd7ac6adf7fa4769ba4db3308624907d77cd","last_reissued_at":"2026-05-17T23:47:16.104605Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:16.104605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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