{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DYDH5DQSJ7QQ3LBGT5LTPFJHNP","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":"d2037d6819fa823db5212251b0e54aa732a41920dbd193929f116e8dc8a269ac","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-05-18T15:13:21Z","title_canon_sha256":"8fbec0c09c5c144b64a973023528166cbf34f2e0c6fe0f8b3e5c778bdd4c559f"},"schema_version":"1.0","source":{"id":"1805.07272","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07272","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07272v2","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07272","created_at":"2026-05-17T23:53:09Z"},{"alias_kind":"pith_short_12","alias_value":"DYDH5DQSJ7QQ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DYDH5DQSJ7QQ3LBG","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DYDH5DQS","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:b74a51e4041a74131c9a3f7fc99135fd7d3f8d9d093a5516d54811f7c7e91c96","target":"graph","created_at":"2026-05-17T23:53:09Z","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":"A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth subgradient-based convex optimization for determining the maximum likelihood density estimate cause long runtimes for dimensions $d \\geq 2$ and large sample sets. The presented approach is based on mildly non-convex smooth approximations of the objective function and \\textit{sparse}, adaptive piecewise-affine density parametrization. Established memory-efficie","authors_text":"Christoph Schn\\\"orr, Fabian Rathke","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-05-18T15:13:21Z","title":"Fast Multivariate Log-Concave Density Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07272","kind":"arxiv","version":2},"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:a80862b82b9c5411e186c8f7e1b87e4b879ff910ea1bf3c437725924ed516702","target":"record","created_at":"2026-05-17T23:53:09Z","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":"d2037d6819fa823db5212251b0e54aa732a41920dbd193929f116e8dc8a269ac","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-05-18T15:13:21Z","title_canon_sha256":"8fbec0c09c5c144b64a973023528166cbf34f2e0c6fe0f8b3e5c778bdd4c559f"},"schema_version":"1.0","source":{"id":"1805.07272","kind":"arxiv","version":2}},"canonical_sha256":"1e067e8e124fe10dac269f573795276bcbaf15b26af3ed17ab8bb0bc00ff7aea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e067e8e124fe10dac269f573795276bcbaf15b26af3ed17ab8bb0bc00ff7aea","first_computed_at":"2026-05-17T23:53:09.563870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:09.563870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4XG3AGk42LN488DsiHp2pteQBFW/c6DtYrT5GAkGIju4FVbyOGb5ZvZ/5q8Y8nNT1fXEEdojbbVmV0MDbbXCDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:09.564421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07272","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a80862b82b9c5411e186c8f7e1b87e4b879ff910ea1bf3c437725924ed516702","sha256:b74a51e4041a74131c9a3f7fc99135fd7d3f8d9d093a5516d54811f7c7e91c96"],"state_sha256":"748ad2a55b3bcaf5420823bc126afec2b8ac11fc5a31984b3f77daec26773093"}