{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XLV46J66AWHZGKZCZPQCY6EQ2L","short_pith_number":"pith:XLV46J66","schema_version":"1.0","canonical_sha256":"baebcf27de058f932b22cbe02c7890d2d7520816730d4dbb0d16e796f8d62705","source":{"kind":"arxiv","id":"1708.00059","version":1},"attestation_state":"computed","paper":{"title":"Asymptotically optimal private estimation under mean square loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander Barg, Min Ye","submitted_at":"2017-07-31T20:31:03Z","abstract_excerpt":"We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw samples from the privatized samples. A positive number $\\epsilon$ measures the privacy level of a privatization scheme.\n  In our previous work (arXiv:1702.00610), we proposed a family of new privatization schemes and the corresponding estimator. We also proved that our scheme and estimator are order optimal in the regime $e^{\\epsilon} \\ll"},"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":"1708.00059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-07-31T20:31:03Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT","stat.TH"],"title_canon_sha256":"099ff1af03e184f09fdf83e610a56045566acae45aa3bbea1b7dfd62905b11d9","abstract_canon_sha256":"dc5b0b5010c9879145c280e3e2f7286c85853d6b8c43cf17bf94ebfd1d85861c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:06.137250Z","signature_b64":"r9HSt6Ac+raR3JhYx2QdvdNAjFdDiWRN4ZsecrQ33ikzowWetbmvCrnFzJleV/9d5aupSSiA377HY991/pPzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baebcf27de058f932b22cbe02c7890d2d7520816730d4dbb0d16e796f8d62705","last_reissued_at":"2026-05-18T00:39:06.136465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:06.136465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotically optimal private estimation under mean square loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander Barg, Min Ye","submitted_at":"2017-07-31T20:31:03Z","abstract_excerpt":"We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw samples from the privatized samples. A positive number $\\epsilon$ measures the privacy level of a privatization scheme.\n  In our previous work (arXiv:1702.00610), we proposed a family of new privatization schemes and the corresponding estimator. We also proved that our scheme and estimator are order optimal in the regime $e^{\\epsilon} \\ll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00059","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":"1708.00059","created_at":"2026-05-18T00:39:06.136601+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.00059v1","created_at":"2026-05-18T00:39:06.136601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00059","created_at":"2026-05-18T00:39:06.136601+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLV46J66AWHZ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLV46J66AWHZGKZC","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLV46J66","created_at":"2026-05-18T12:31:56.362134+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/XLV46J66AWHZGKZCZPQCY6EQ2L","json":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L.json","graph_json":"https://pith.science/api/pith-number/XLV46J66AWHZGKZCZPQCY6EQ2L/graph.json","events_json":"https://pith.science/api/pith-number/XLV46J66AWHZGKZCZPQCY6EQ2L/events.json","paper":"https://pith.science/paper/XLV46J66"},"agent_actions":{"view_html":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L","download_json":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L.json","view_paper":"https://pith.science/paper/XLV46J66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.00059&json=true","fetch_graph":"https://pith.science/api/pith-number/XLV46J66AWHZGKZCZPQCY6EQ2L/graph.json","fetch_events":"https://pith.science/api/pith-number/XLV46J66AWHZGKZCZPQCY6EQ2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L/action/storage_attestation","attest_author":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L/action/author_attestation","sign_citation":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L/action/citation_signature","submit_replication":"https://pith.science/pith/XLV46J66AWHZGKZCZPQCY6EQ2L/action/replication_record"}},"created_at":"2026-05-18T00:39:06.136601+00:00","updated_at":"2026-05-18T00:39:06.136601+00:00"}