{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5Z54SAJ2I3J4YP5VH6SCZAMLC4","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":"0c91ead31629888fc67eeb3ac26436a632d89e0827ab816a33418a43ea187b5e","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-06-16T03:34:14Z","title_canon_sha256":"8aea7cfd30e2d1e0034954a08fa6e2851443338b53eef686ce9346fb9e197842"},"schema_version":"1.0","source":{"id":"2106.08537","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.08537","created_at":"2026-07-05T03:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"2106.08537v2","created_at":"2026-07-05T03:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.08537","created_at":"2026-07-05T03:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"5Z54SAJ2I3J4","created_at":"2026-07-05T03:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"5Z54SAJ2I3J4YP5V","created_at":"2026-07-05T03:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"5Z54SAJ2","created_at":"2026-07-05T03:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:4c20df62d6132192222acd374f7ba45d1f69ceddf820111e1a0cb32d1482c3a5","target":"graph","created_at":"2026-07-05T03:31:03Z","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/2106.08537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\\mathbb{R}^d$ and a parameter $0< \\alpha <\\frac 1 2$ such that an $\\alpha$-fraction of the points in $T$ are i.i.d. samples from a well-behaved distribution $\\mathcal{D}$ and the remaining $(1-\\alpha)$-fraction are arbitrary. The goal is to output a small list of vectors, at least one of which is close to the mean of $\\mathcal{D}$. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistica","authors_text":"Daniel Kongsgaard, Daniel M. Kane, Ilias Diakonikolas, Jerry Li, Kevin Tian","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-06-16T03:34:14Z","title":"Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08537","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:e7723c8f341486ff12cd27d3d36925f30b9ff5a32d4519d2512dde3bf6cae49f","target":"record","created_at":"2026-07-05T03:31:03Z","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":"0c91ead31629888fc67eeb3ac26436a632d89e0827ab816a33418a43ea187b5e","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-06-16T03:34:14Z","title_canon_sha256":"8aea7cfd30e2d1e0034954a08fa6e2851443338b53eef686ce9346fb9e197842"},"schema_version":"1.0","source":{"id":"2106.08537","kind":"arxiv","version":2}},"canonical_sha256":"ee7bc9013a46d3cc3fb53fa42c818b173ba2574411b4e6779a0c6a3dae758ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7bc9013a46d3cc3fb53fa42c818b173ba2574411b4e6779a0c6a3dae758ccc","first_computed_at":"2026-07-05T03:31:03.267905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:03.267905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgvqjhlb5MbneIwDCmqyDL5kf2dGgec+4CL+2tFAu0Gy9xDF69TOoiFi7jV0H4FYZaen2tr6TRezRi6UAgb7BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:03.268534Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.08537","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7723c8f341486ff12cd27d3d36925f30b9ff5a32d4519d2512dde3bf6cae49f","sha256:4c20df62d6132192222acd374f7ba45d1f69ceddf820111e1a0cb32d1482c3a5"],"state_sha256":"d457884c44a838a314faa0296aa8aa8a609020075d4ec9639d67e4258b19963c"}