{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LKF2ZXMSTLKCPSOL6RDQJPMO3G","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":"c14e9bc4461eb1814e104c57248102be3c596efe1d74728899fa98e5f797a426","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-26T08:31:18Z","title_canon_sha256":"33b0af5b0a0fe1ed3cbe23350d432560b252ebe017e716443aa935e0def68678"},"schema_version":"1.0","source":{"id":"1605.08188","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08188","created_at":"2026-05-18T00:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08188v2","created_at":"2026-05-18T00:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08188","created_at":"2026-05-18T00:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"LKF2ZXMSTLKC","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LKF2ZXMSTLKCPSOL","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LKF2ZXMS","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:57ba4bc0a9efb8c2ba7bda9c3831790c8703421cf653474065d61b8674532bd4","target":"graph","created_at":"2026-05-18T00:43:02Z","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 study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on $\\mathbb{R}^d$, for all $d \\geq 1$. Prior to our work, no upper bound on the sample complexity of this learning problem was known for the case of $d>3$. In more detail, we give an estimator that, for any $d \\ge 1$ and $\\epsilon>0$, draws $\\tilde{O}_d \\left( (1/\\epsilon)^{(d+5)/2} \\right)$ samples from an unknown target log-concave density on $\\mathbb{R}^d$, and outputs a hypothesis that (with high probability) is $\\eps","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-26T08:31:18Z","title":"Learning Multivariate Log-concave Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08188","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":"sha256:34ded29aa57d927e74a15b454731cb687b4c4d0bb20bb0cf40919645439ae939","target":"record","created_at":"2026-05-18T00:43:02Z","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":"c14e9bc4461eb1814e104c57248102be3c596efe1d74728899fa98e5f797a426","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-05-26T08:31:18Z","title_canon_sha256":"33b0af5b0a0fe1ed3cbe23350d432560b252ebe017e716443aa935e0def68678"},"schema_version":"1.0","source":{"id":"1605.08188","kind":"arxiv","version":2}},"canonical_sha256":"5a8bacdd929ad427c9cbf44704bd8ed9ad8a016d54832cb6b3144899b1446822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a8bacdd929ad427c9cbf44704bd8ed9ad8a016d54832cb6b3144899b1446822","first_computed_at":"2026-05-18T00:43:02.788335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:02.788335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zm2VV7KJvdNsqV+oPxCSKxQfXOWofTX1a4LVZynR7LsHHt9dqJRf8+6x+EhaS61bXWPHWiCgk4StviIYqIU4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:02.788903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08188","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34ded29aa57d927e74a15b454731cb687b4c4d0bb20bb0cf40919645439ae939","sha256:57ba4bc0a9efb8c2ba7bda9c3831790c8703421cf653474065d61b8674532bd4"],"state_sha256":"0545d6d9335003b02239d9e719afb996586f659b7da39479535c23c80e138bbd"}