{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:B6AD5AIWILTTW3FJAB2JRLBRYD","short_pith_number":"pith:B6AD5AIW","schema_version":"1.0","canonical_sha256":"0f803e811642e73b6ca9007498ac31c0f52e45f166274303054450e34e017adf","source":{"kind":"arxiv","id":"1205.4697","version":5},"attestation_state":"computed","paper":{"title":"Inference using noisy degrees: Differentially private $\\beta$-model and synthetic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"stat.ME","authors_text":"Aleksandra Slavkovi\\'c, Vishesh Karwa","submitted_at":"2012-05-21T19:13:13Z","abstract_excerpt":"The $\\beta$-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the $\\beta$-model, and show that the MLE never exists for the degree partition $\\beta$-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of $\\beta$-model, and show it is consistent and asymptotically normally distributed - it achieves the same ra"},"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":"1205.4697","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-05-21T19:13:13Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"39f2e763b27bcf1279b45baa75582b13ed694402a4df751862f4809063be5f9f","abstract_canon_sha256":"d5b6078c47ab92213507d4de3d41ef5f3cbcf56e5faa9f5a913418359fd931b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:04.689394Z","signature_b64":"96MfreQasA4jQgoRyKC2egrKI4DtKW+GsTRQBDL8B8xQ5kqNt3iSdeRwpuBUhY3n0AXmEJzmquxCz5Ka/dVFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f803e811642e73b6ca9007498ac31c0f52e45f166274303054450e34e017adf","last_reissued_at":"2026-05-18T01:23:04.688734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:04.688734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inference using noisy degrees: Differentially private $\\beta$-model and synthetic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"stat.ME","authors_text":"Aleksandra Slavkovi\\'c, Vishesh Karwa","submitted_at":"2012-05-21T19:13:13Z","abstract_excerpt":"The $\\beta$-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the $\\beta$-model, and show that the MLE never exists for the degree partition $\\beta$-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of $\\beta$-model, and show it is consistent and asymptotically normally distributed - it achieves the same ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4697","kind":"arxiv","version":5},"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":"1205.4697","created_at":"2026-05-18T01:23:04.688845+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4697v5","created_at":"2026-05-18T01:23:04.688845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4697","created_at":"2026-05-18T01:23:04.688845+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6AD5AIWILTT","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6AD5AIWILTTW3FJ","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6AD5AIW","created_at":"2026-05-18T12:26:58.693483+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/B6AD5AIWILTTW3FJAB2JRLBRYD","json":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD.json","graph_json":"https://pith.science/api/pith-number/B6AD5AIWILTTW3FJAB2JRLBRYD/graph.json","events_json":"https://pith.science/api/pith-number/B6AD5AIWILTTW3FJAB2JRLBRYD/events.json","paper":"https://pith.science/paper/B6AD5AIW"},"agent_actions":{"view_html":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD","download_json":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD.json","view_paper":"https://pith.science/paper/B6AD5AIW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4697&json=true","fetch_graph":"https://pith.science/api/pith-number/B6AD5AIWILTTW3FJAB2JRLBRYD/graph.json","fetch_events":"https://pith.science/api/pith-number/B6AD5AIWILTTW3FJAB2JRLBRYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD/action/storage_attestation","attest_author":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD/action/author_attestation","sign_citation":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD/action/citation_signature","submit_replication":"https://pith.science/pith/B6AD5AIWILTTW3FJAB2JRLBRYD/action/replication_record"}},"created_at":"2026-05-18T01:23:04.688845+00:00","updated_at":"2026-05-18T01:23:04.688845+00:00"}