{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4OFRIASMMNPAD7EH3WAU2HC77D","short_pith_number":"pith:4OFRIASM","schema_version":"1.0","canonical_sha256":"e38b14024c635e01fc87dd814d1c5ff8fc2dea232c98e579536aced3431d1337","source":{"kind":"arxiv","id":"1505.00199","version":4},"attestation_state":"computed","paper":{"title":"Theory of Optimizing Pseudolinear Performance Measures: Application to F-measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nicolas Usunier, Shameem A Puthiya Parambath, Yves Grandvalet","submitted_at":"2015-05-01T15:25:59Z","abstract_excerpt":"Non-linear performance measures are widely used for the evaluation of learning algorithms. For example, $F$-measure is a commonly used performance measure for classification problems in machine learning and information retrieval community. We study the theoretical properties of a subset of non-linear performance measures called pseudo-linear performance measures which includes $F$-measure, \\emph{Jaccard Index}, among many others. We establish that many notions of $F$-measures and \\emph{Jaccard Index} are pseudo-linear functions of the per-class false negatives and false positives for binary, 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":"1505.00199","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-05-01T15:25:59Z","cross_cats_sorted":[],"title_canon_sha256":"ef7b26b913f9bdfe1c90772db9508fc05c63066bd53f1a4bb2d68739532b15b4","abstract_canon_sha256":"1c49bc8cd7cd2167abb7d2157975f8a5b5fdfa0a90c5a9c84acbeeed92d63570"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:03.202449Z","signature_b64":"M5ayHqxiQTP9GIyYh3tW2xd3evQ4XFBBvkUwh3E+w/TV7GhR7gW6lvWVSpNNvCOW4TtyZA7R++wGBv8guWfLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e38b14024c635e01fc87dd814d1c5ff8fc2dea232c98e579536aced3431d1337","last_reissued_at":"2026-05-18T00:27:03.201935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:03.201935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theory of Optimizing Pseudolinear Performance Measures: Application to F-measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nicolas Usunier, Shameem A Puthiya Parambath, Yves Grandvalet","submitted_at":"2015-05-01T15:25:59Z","abstract_excerpt":"Non-linear performance measures are widely used for the evaluation of learning algorithms. For example, $F$-measure is a commonly used performance measure for classification problems in machine learning and information retrieval community. We study the theoretical properties of a subset of non-linear performance measures called pseudo-linear performance measures which includes $F$-measure, \\emph{Jaccard Index}, among many others. We establish that many notions of $F$-measures and \\emph{Jaccard Index} are pseudo-linear functions of the per-class false negatives and false positives for binary, m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00199","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.00199","created_at":"2026-05-18T00:27:03.202034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00199v4","created_at":"2026-05-18T00:27:03.202034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00199","created_at":"2026-05-18T00:27:03.202034+00:00"},{"alias_kind":"pith_short_12","alias_value":"4OFRIASMMNPA","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4OFRIASMMNPAD7EH","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4OFRIASM","created_at":"2026-05-18T12:29:05.191682+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/4OFRIASMMNPAD7EH3WAU2HC77D","json":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D.json","graph_json":"https://pith.science/api/pith-number/4OFRIASMMNPAD7EH3WAU2HC77D/graph.json","events_json":"https://pith.science/api/pith-number/4OFRIASMMNPAD7EH3WAU2HC77D/events.json","paper":"https://pith.science/paper/4OFRIASM"},"agent_actions":{"view_html":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D","download_json":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D.json","view_paper":"https://pith.science/paper/4OFRIASM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00199&json=true","fetch_graph":"https://pith.science/api/pith-number/4OFRIASMMNPAD7EH3WAU2HC77D/graph.json","fetch_events":"https://pith.science/api/pith-number/4OFRIASMMNPAD7EH3WAU2HC77D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D/action/storage_attestation","attest_author":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D/action/author_attestation","sign_citation":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D/action/citation_signature","submit_replication":"https://pith.science/pith/4OFRIASMMNPAD7EH3WAU2HC77D/action/replication_record"}},"created_at":"2026-05-18T00:27:03.202034+00:00","updated_at":"2026-05-18T00:27:03.202034+00:00"}