{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Z7UJHMTXG3BGC7Y6R5KWGRH4PQ","short_pith_number":"pith:Z7UJHMTX","schema_version":"1.0","canonical_sha256":"cfe893b27736c2617f1e8f556344fc7c21a58a99d6a55f19839f98686c56288b","source":{"kind":"arxiv","id":"1711.01566","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Submodular Maximization: The Case of Coverage Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Krause, Hamed Hassani, Mario Lucic, Mohammad Reza Karimi","submitted_at":"2017-11-05T11:58:55Z","abstract_excerpt":"Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, namely stochastic gradient descent and its variants, to such discrete problems. We first introduce the problem of stochastic submodular optimization, where one needs to optimize a submodular objective which is given as an expectation. Our model captures situations where the discrete objective arises as an empirical risk (e.g., in the case 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":"1711.01566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-11-05T11:58:55Z","cross_cats_sorted":["cs.DM","stat.ML"],"title_canon_sha256":"db3c29d7801881db3de778cce59485ba034782b581f5c4afd95a5ad6fa755f74","abstract_canon_sha256":"2d1e405cfbf3017aef14f4e8cffb4b2031740907111cadc5beab38144d6d06ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:17.457131Z","signature_b64":"krIJMJgsJc6DD/fOLbMjz16O8aAZpb7fajo1qZkVY0UvdnofTqUQGGRJDeKqaSfYl79GdNrDaRfQOmVwmNvwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe893b27736c2617f1e8f556344fc7c21a58a99d6a55f19839f98686c56288b","last_reissued_at":"2026-05-18T00:31:17.456436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:17.456436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Submodular Maximization: The Case of Coverage Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andreas Krause, Hamed Hassani, Mario Lucic, Mohammad Reza Karimi","submitted_at":"2017-11-05T11:58:55Z","abstract_excerpt":"Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, namely stochastic gradient descent and its variants, to such discrete problems. We first introduce the problem of stochastic submodular optimization, where one needs to optimize a submodular objective which is given as an expectation. Our model captures situations where the discrete objective arises as an empirical risk (e.g., in the case o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01566","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":"1711.01566","created_at":"2026-05-18T00:31:17.456551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.01566v1","created_at":"2026-05-18T00:31:17.456551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01566","created_at":"2026-05-18T00:31:17.456551+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7UJHMTXG3BG","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7UJHMTXG3BGC7Y6","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7UJHMTX","created_at":"2026-05-18T12:31:59.375834+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/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ","json":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ.json","graph_json":"https://pith.science/api/pith-number/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/graph.json","events_json":"https://pith.science/api/pith-number/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/events.json","paper":"https://pith.science/paper/Z7UJHMTX"},"agent_actions":{"view_html":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ","download_json":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ.json","view_paper":"https://pith.science/paper/Z7UJHMTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.01566&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/action/storage_attestation","attest_author":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/action/author_attestation","sign_citation":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/action/citation_signature","submit_replication":"https://pith.science/pith/Z7UJHMTXG3BGC7Y6R5KWGRH4PQ/action/replication_record"}},"created_at":"2026-05-18T00:31:17.456551+00:00","updated_at":"2026-05-18T00:31:17.456551+00:00"}