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Place the most influential variable $x_i$ of $f$ at the root, and recurse on the subfunctions $f_{x_i=0}$ and $f_{x_i=1}$ on the left and right subtrees respectively; terminate once the tree is an $\\varepsilon$-approximation of $f$. We analyze the quality of this heuristic, obtaining near-matching upper and lower bounds:\n  $\\circ$ Upper bound: For every $f$ with decision tree size $s$ and every $\\varepsilon \\in (0,\\frac1{2})$, this heuristic builds a decision tree of size at most $s^{O(\\"},"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":"1911.07375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-11-18T00:25:31Z","cross_cats_sorted":["cs.CC","cs.LG"],"title_canon_sha256":"6ba0231cc2f085d0a3ca28f97b4dd6e333a11a9c3b90995fec4eb29ebfbefbe6","abstract_canon_sha256":"a371b205b5f918980d5bd72fc103dd3d965fc22d48c68346c9c4f9c443f8c10a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:46.266701Z","signature_b64":"qy4gG+F7O2Oi8l037zk92YzUqg7/pCpZ/RuJcYiutgAuzSImNuSf4kXmCeOPhpYRpwz1lrgCCvlIZtpEkGIvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e131c1d0497aecb4c83439a2788ab959659904ab30f375c12461ff20a5281f8","last_reissued_at":"2026-07-05T00:19:46.266290Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:46.266290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Top-down induction of decision trees: rigorous guarantees and inherent limitations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG"],"primary_cat":"cs.DS","authors_text":"Guy Blanc, Jane Lange, Li-Yang Tan","submitted_at":"2019-11-18T00:25:31Z","abstract_excerpt":"Consider the following heuristic for building a decision tree for a function $f : \\{0,1\\}^n \\to \\{\\pm 1\\}$. 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We analyze the quality of this heuristic, obtaining near-matching upper and lower bounds:\n  $\\circ$ Upper bound: For every $f$ with decision tree size $s$ and every $\\varepsilon \\in (0,\\frac1{2})$, this heuristic builds a decision tree of size at most $s^{O(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07375","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.07375/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1911.07375","created_at":"2026-07-05T00:19:46.266364+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.07375v1","created_at":"2026-07-05T00:19:46.266364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.07375","created_at":"2026-07-05T00:19:46.266364+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYJRYHIES6XM","created_at":"2026-07-05T00:19:46.266364+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYJRYHIES6XMWTED","created_at":"2026-07-05T00:19:46.266364+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYJRYHIE","created_at":"2026-07-05T00:19:46.266364+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW","json":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW.json","graph_json":"https://pith.science/api/pith-number/TYJRYHIES6XMWTEDIONCPCFLSW/graph.json","events_json":"https://pith.science/api/pith-number/TYJRYHIES6XMWTEDIONCPCFLSW/events.json","paper":"https://pith.science/paper/TYJRYHIE"},"agent_actions":{"view_html":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW","download_json":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW.json","view_paper":"https://pith.science/paper/TYJRYHIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.07375&json=true","fetch_graph":"https://pith.science/api/pith-number/TYJRYHIES6XMWTEDIONCPCFLSW/graph.json","fetch_events":"https://pith.science/api/pith-number/TYJRYHIES6XMWTEDIONCPCFLSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW/action/storage_attestation","attest_author":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW/action/author_attestation","sign_citation":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW/action/citation_signature","submit_replication":"https://pith.science/pith/TYJRYHIES6XMWTEDIONCPCFLSW/action/replication_record"}},"created_at":"2026-07-05T00:19:46.266364+00:00","updated_at":"2026-07-05T00:19:46.266364+00:00"}