{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:FXZGLO46VYXV2SDFC4SXTEBFXT","short_pith_number":"pith:FXZGLO46","schema_version":"1.0","canonical_sha256":"2df265bb9eae2f5d48651725799025bcd269707586c76c86dad40f97e47a8d2c","source":{"kind":"arxiv","id":"2006.01293","version":1},"attestation_state":"computed","paper":{"title":"From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Krause, Aytunc Sahin, Joachim M. Buhmann, Yatao Bian","submitted_at":"2020-06-01T22:20:45Z","abstract_excerpt":"Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension"},"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":"2006.01293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-01T22:20:45Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"66bc22a49da35a21159040a17161d57c7b41c6525099d551f7c96ce524395fa4","abstract_canon_sha256":"a68667b294c52da997b58294fdffc8216e79b3537eeca9be148855d8e793b94a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:16.019230Z","signature_b64":"YVcOWUsTZVRR0dFD+uLfWG9kx3cQK1YphWxDi2b8F4ICki/3STF5Fw9H4Ocd18xOQRD0R7HALEvXZWypdWjCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df265bb9eae2f5d48651725799025bcd269707586c76c86dad40f97e47a8d2c","last_reissued_at":"2026-07-05T01:07:16.018838Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:16.018838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Sets to Multisets: Provable Variational Inference for Probabilistic Integer Submodular Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Krause, Aytunc Sahin, Joachim M. Buhmann, Yatao Bian","submitted_at":"2020-06-01T22:20:45Z","abstract_excerpt":"Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01293","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/2006.01293/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":"2006.01293","created_at":"2026-07-05T01:07:16.018901+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.01293v1","created_at":"2026-07-05T01:07:16.018901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.01293","created_at":"2026-07-05T01:07:16.018901+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXZGLO46VYXV","created_at":"2026-07-05T01:07:16.018901+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXZGLO46VYXV2SDF","created_at":"2026-07-05T01:07:16.018901+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXZGLO46","created_at":"2026-07-05T01:07:16.018901+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/FXZGLO46VYXV2SDFC4SXTEBFXT","json":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT.json","graph_json":"https://pith.science/api/pith-number/FXZGLO46VYXV2SDFC4SXTEBFXT/graph.json","events_json":"https://pith.science/api/pith-number/FXZGLO46VYXV2SDFC4SXTEBFXT/events.json","paper":"https://pith.science/paper/FXZGLO46"},"agent_actions":{"view_html":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT","download_json":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT.json","view_paper":"https://pith.science/paper/FXZGLO46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.01293&json=true","fetch_graph":"https://pith.science/api/pith-number/FXZGLO46VYXV2SDFC4SXTEBFXT/graph.json","fetch_events":"https://pith.science/api/pith-number/FXZGLO46VYXV2SDFC4SXTEBFXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT/action/storage_attestation","attest_author":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT/action/author_attestation","sign_citation":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT/action/citation_signature","submit_replication":"https://pith.science/pith/FXZGLO46VYXV2SDFC4SXTEBFXT/action/replication_record"}},"created_at":"2026-07-05T01:07:16.018901+00:00","updated_at":"2026-07-05T01:07:16.018901+00:00"}