{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:J5CX4YTI3XLFLPILTMSGZW4DUT","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":"2c2e131adbeb99ff39a06d7ad3683d8e437b0bf94eaca3d80d14cae0b8cd701d","cross_cats_sorted":["cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-12-03T17:54:03Z","title_canon_sha256":"c6ba7647b1f80aabd7665d12390a2989f02ac472cf19d9bda7fc0e71e33afb6e"},"schema_version":"1.0","source":{"id":"2012.02119","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.02119","created_at":"2026-07-05T02:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"2012.02119v3","created_at":"2026-07-05T02:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.02119","created_at":"2026-07-05T02:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"J5CX4YTI3XLF","created_at":"2026-07-05T02:46:43Z"},{"alias_kind":"pith_short_16","alias_value":"J5CX4YTI3XLFLPIL","created_at":"2026-07-05T02:46:43Z"},{"alias_kind":"pith_short_8","alias_value":"J5CX4YTI","created_at":"2026-07-05T02:46:43Z"}],"graph_snapshots":[{"event_id":"sha256:5ef09ee13d779287be5bfba6d5c0de1cfb1e30b6f2aa4dd7bc1af587afd820cb","target":"graph","created_at":"2026-07-05T02:46:43Z","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/2012.02119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main open problem in several previous works on algorithmic robust statistics, which addressed the special cases of robustly estimating (a) a single Gaussian, (b) a mixture of TV-distance separated Gaussians, and (c) a uniform mixture of two Gaussians. Our main tools are an efficient \\emph{partial clustering} algorithm that relies on the sum-of-squares method, and a","authors_text":"Ainesh Bakshi, Daniel M. Kane, He Jia, Ilias Diakonikolas, Pravesh K. Kothari, Santosh S. Vempala","cross_cats":["cs.LG","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-12-03T17:54:03Z","title":"Robustly Learning Mixtures of $k$ Arbitrary Gaussians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.02119","kind":"arxiv","version":3},"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:d41b60342b22bf424d4dac5a449ea5d0c3a0f2076b31eb8c2ef52ed2095852cc","target":"record","created_at":"2026-07-05T02:46:43Z","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":"2c2e131adbeb99ff39a06d7ad3683d8e437b0bf94eaca3d80d14cae0b8cd701d","cross_cats_sorted":["cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-12-03T17:54:03Z","title_canon_sha256":"c6ba7647b1f80aabd7665d12390a2989f02ac472cf19d9bda7fc0e71e33afb6e"},"schema_version":"1.0","source":{"id":"2012.02119","kind":"arxiv","version":3}},"canonical_sha256":"4f457e6268ddd655bd0b9b246cdb83a4d859e0fa1d3fbebabdbb2a0ff1f8d145","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f457e6268ddd655bd0b9b246cdb83a4d859e0fa1d3fbebabdbb2a0ff1f8d145","first_computed_at":"2026-07-05T02:46:43.283034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:46:43.283034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6kuTtw7+3er5rpJYHfC0vnFLD/8O4FN6XwvgWj0YM5Trrf4X+xcty+K5/jDYxtCrYNxZyIQVUArrzC0pXLlLDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:46:43.283493Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.02119","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d41b60342b22bf424d4dac5a449ea5d0c3a0f2076b31eb8c2ef52ed2095852cc","sha256:5ef09ee13d779287be5bfba6d5c0de1cfb1e30b6f2aa4dd7bc1af587afd820cb"],"state_sha256":"2a2c3b5c460c9c968ad8adf9c55a2b7a35d9d7374645d0e81dd931f6eb44e8fd"}