{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JEEBM2TXGLI2ULH6RX5DSVC4CZ","short_pith_number":"pith:JEEBM2TX","schema_version":"1.0","canonical_sha256":"4908166a7732d1aa2cfe8dfa39545c165923011af5dafa78e77d5c82cd58cfe7","source":{"kind":"arxiv","id":"1408.2051","version":1},"attestation_state":"computed","paper":{"title":"Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Jeff A. Bilmes, Rishabh Iyer","submitted_at":"2014-08-09T05:48:31Z","abstract_excerpt":"We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a dierence between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the multiplica"},"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":"1408.2051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:48:31Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c02257e7711b2a4f828185f79444859829ac4edc704fc4e008a4c18047476b02","abstract_canon_sha256":"b5366eb02c8aad9afb5e14b9c80516e841a4a43953a233c53628d8b6599b145e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:30.539748Z","signature_b64":"2Qym32uMMqRMfkDFWvhDMm7yxEh9tUFBcJipwtGE3iToQVOFK6Yl6F3dU7BWIQ2OvwC8IwzR5vlpwDKPAHZYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4908166a7732d1aa2cfe8dfa39545c165923011af5dafa78e77d5c82cd58cfe7","last_reissued_at":"2026-05-18T02:45:30.539157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:30.539157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Jeff A. Bilmes, Rishabh Iyer","submitted_at":"2014-08-09T05:48:31Z","abstract_excerpt":"We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a dierence between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the multiplica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2051","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.2051","created_at":"2026-05-18T02:45:30.539230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2051v1","created_at":"2026-05-18T02:45:30.539230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2051","created_at":"2026-05-18T02:45:30.539230+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEEBM2TXGLI2","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEEBM2TXGLI2ULH6","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEEBM2TX","created_at":"2026-05-18T12:28:33.132498+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/JEEBM2TXGLI2ULH6RX5DSVC4CZ","json":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ.json","graph_json":"https://pith.science/api/pith-number/JEEBM2TXGLI2ULH6RX5DSVC4CZ/graph.json","events_json":"https://pith.science/api/pith-number/JEEBM2TXGLI2ULH6RX5DSVC4CZ/events.json","paper":"https://pith.science/paper/JEEBM2TX"},"agent_actions":{"view_html":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ","download_json":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ.json","view_paper":"https://pith.science/paper/JEEBM2TX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2051&json=true","fetch_graph":"https://pith.science/api/pith-number/JEEBM2TXGLI2ULH6RX5DSVC4CZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JEEBM2TXGLI2ULH6RX5DSVC4CZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ/action/storage_attestation","attest_author":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ/action/author_attestation","sign_citation":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ/action/citation_signature","submit_replication":"https://pith.science/pith/JEEBM2TXGLI2ULH6RX5DSVC4CZ/action/replication_record"}},"created_at":"2026-05-18T02:45:30.539230+00:00","updated_at":"2026-05-18T02:45:30.539230+00:00"}