{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BEGRBWJNEZXPEZAOXOBKRHEWLH","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":"bf85b07f0acf71683bd532f17fa25320021d659e95eb35814b61c356386622fc","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-03-26T03:36:36Z","title_canon_sha256":"1b06c966d4957b3e55bbb1940925947ce0dc40c5bf9232ce20c5ae8b9b0e029f"},"schema_version":"1.0","source":{"id":"2503.20193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.20193","created_at":"2026-07-05T10:39:34Z"},{"alias_kind":"arxiv_version","alias_value":"2503.20193v1","created_at":"2026-07-05T10:39:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.20193","created_at":"2026-07-05T10:39:34Z"},{"alias_kind":"pith_short_12","alias_value":"BEGRBWJNEZXP","created_at":"2026-07-05T10:39:34Z"},{"alias_kind":"pith_short_16","alias_value":"BEGRBWJNEZXPEZAO","created_at":"2026-07-05T10:39:34Z"},{"alias_kind":"pith_short_8","alias_value":"BEGRBWJN","created_at":"2026-07-05T10:39:34Z"}],"graph_snapshots":[{"event_id":"sha256:c49b9d6a4fdb736fdeeeecfc1373a5501eb817590dd17fa47f496e0e2e0da29b","target":"graph","created_at":"2026-07-05T10:39:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.20193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the nonparametric maximum likelihood estimator $\\widehat{\\pi}$ for Gaussian location mixtures in one dimension. It has been known since (Lindsay, 1983) that given an $n$-point dataset, this estimator always returns a mixture with at most $n$ components, and more recently (Wu-Polyanskiy, 2020) gave a sharp $O(\\log n)$ bound for subgaussian data. In this work we study computational aspects of $\\widehat{\\pi}$. We provide an algorithm which for small enough $\\varepsilon>0$ computes an $\\varepsilon$-approximation of $\\widehat\\pi$ in Wasserstein distance in time $K+Cnk^2\\log\\log(1/\\varepsil","authors_text":"Mark Sellke, Yury Polyanskiy","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-03-26T03:36:36Z","title":"Nonparametric MLE for Gaussian Location Mixtures: Certified Computation and Generic Behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.20193","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":"sha256:792596af6a8897e3648bcecd68d82685689d16780e47944d49ae27dbd3f83c8d","target":"record","created_at":"2026-07-05T10:39:34Z","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":"bf85b07f0acf71683bd532f17fa25320021d659e95eb35814b61c356386622fc","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-03-26T03:36:36Z","title_canon_sha256":"1b06c966d4957b3e55bbb1940925947ce0dc40c5bf9232ce20c5ae8b9b0e029f"},"schema_version":"1.0","source":{"id":"2503.20193","kind":"arxiv","version":1}},"canonical_sha256":"090d10d92d266ef2640ebb82a89c9659dc2ff0324b0e87645283c35a89445187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"090d10d92d266ef2640ebb82a89c9659dc2ff0324b0e87645283c35a89445187","first_computed_at":"2026-07-05T10:39:34.320376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:39:34.320376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IPEgr1pirUds69kcv39zJDAPLimo+JL4X3fnmwINIWvSNFVRzlkWFr8D0hjyz4wrDrnRy5fef1j04TJ+ZmN8Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:39:34.320857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.20193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:792596af6a8897e3648bcecd68d82685689d16780e47944d49ae27dbd3f83c8d","sha256:c49b9d6a4fdb736fdeeeecfc1373a5501eb817590dd17fa47f496e0e2e0da29b"],"state_sha256":"c2e5edfecdff78817893d8903d93a999c4cc0396ab423d3bf51f64c2571e556c"}