{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WNLRNTJGAZJXTHRU5AMH45N6IE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c808e32b35f8e1276b9e75d14e3eca2a302247113a2482265850daa5dac9faaa","cross_cats_sorted":["cs.CR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-05T16:33:51Z","title_canon_sha256":"013b022ff4c08b65112d38b8199cd5a6112f93576f0115f2e52703f2dc2e7af9"},"schema_version":"1.0","source":{"id":"1903.01927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01927","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01927v1","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01927","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"WNLRNTJGAZJX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WNLRNTJGAZJXTHRU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WNLRNTJG","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:ce78e4cbd816da9633c62550e91015d277f325bc1fbd69fe8a9c9196fa574662","target":"graph","created_at":"2026-05-17T23:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We address the problem of non-parametric density estimation under the additional constraint that only privatised data are allowed to be published and available for inference. For this purpose, we adopt a recent generalisation of classical minimax theory to the framework of local $\\alpha$-differential privacy and provide a lower bound on the rate of convergence over Besov spaces $B^s_{pq}$ under mean integrated $\\mathbb L^r$-risk. This lower bound is deteriorated compared to the standard setup without privacy, and reveals a twofold elbow effect. In order to fulfil the privacy requirement, we su","authors_text":"Adrien Saumard, Amandine Dubois, Cristina Butucea, Martin Kroll","cross_cats":["cs.CR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-05T16:33:51Z","title":"Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01927","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b4df5ee2efb8ca48aa2d870ee0ed5fa5d96d9beddebd5872c6710f6aad7622e1","target":"record","created_at":"2026-05-17T23:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c808e32b35f8e1276b9e75d14e3eca2a302247113a2482265850daa5dac9faaa","cross_cats_sorted":["cs.CR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-05T16:33:51Z","title_canon_sha256":"013b022ff4c08b65112d38b8199cd5a6112f93576f0115f2e52703f2dc2e7af9"},"schema_version":"1.0","source":{"id":"1903.01927","kind":"arxiv","version":1}},"canonical_sha256":"b35716cd260653799e34e8187e75be41186bc19245c17bee3701f3ed39716110","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b35716cd260653799e34e8187e75be41186bc19245c17bee3701f3ed39716110","first_computed_at":"2026-05-17T23:51:59.419538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:59.419538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xuFa6lqGxaEFG+OQ35tcsY7s0TBgOA+27aHHSgjas0pXk/SHscBIDoyMt0uYY91WwjcqvpGWe+im1+ErFpywDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:59.419927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4df5ee2efb8ca48aa2d870ee0ed5fa5d96d9beddebd5872c6710f6aad7622e1","sha256:ce78e4cbd816da9633c62550e91015d277f325bc1fbd69fe8a9c9196fa574662"],"state_sha256":"71d3ad1acee6106dcb224cc2c57cdcc258368f3a4ffdd8d67f3ab90f0715dd3e"}