{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C4OBC2KGJD243Q5H6A5VOE6Q3I","short_pith_number":"pith:C4OBC2KG","canonical_record":{"source":{"id":"1802.07895","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-22T03:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"26397b795c29fd34274272c6264006ceeba66644e4241fa0e48fccc67e7e45e8","abstract_canon_sha256":"10a3625797a18b93ef7fe5f2fd267ccf82313357c9de305ef1149530ac5adb57"},"schema_version":"1.0"},"canonical_sha256":"171c11694648f5cdc3a7f03b5713d0da1585f9f13738c49fa28992a79c64f311","source":{"kind":"arxiv","id":"1802.07895","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07895","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07895v3","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07895","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"C4OBC2KGJD24","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_16","alias_value":"C4OBC2KGJD243Q5H","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_8","alias_value":"C4OBC2KG","created_at":"2026-07-05T00:51:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C4OBC2KGJD243Q5H6A5VOE6Q3I","target":"record","payload":{"canonical_record":{"source":{"id":"1802.07895","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-22T03:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"26397b795c29fd34274272c6264006ceeba66644e4241fa0e48fccc67e7e45e8","abstract_canon_sha256":"10a3625797a18b93ef7fe5f2fd267ccf82313357c9de305ef1149530ac5adb57"},"schema_version":"1.0"},"canonical_sha256":"171c11694648f5cdc3a7f03b5713d0da1585f9f13738c49fa28992a79c64f311","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:51:00.492578Z","signature_b64":"+xBoQ3XAF/WXzmM7xNMaxJLfEAdKVN/tDZ2E3U/D0lfVN5UD3XXYhDB2jD9Zh1IYePjdiyt6CXFGyxTDbcAlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"171c11694648f5cdc3a7f03b5713d0da1585f9f13738c49fa28992a79c64f311","last_reissued_at":"2026-07-05T00:51:00.492119Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:51:00.492119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.07895","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7BKMRtrby4Z8plq8/rzU5w+/6zn6nWfwWn7GZcMvDh3uhC3wC0T2pcyNcT9zVRxcrPuxoiVYMHIB33h/UdCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:29:21.275305Z"},"content_sha256":"fa40776ee635e1e1ec64fafd6a9d9151ea8350f1e248d9bb97d347de49d3408d","schema_version":"1.0","event_id":"sha256:fa40776ee635e1e1ec64fafd6a9d9151ea8350f1e248d9bb97d347de49d3408d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C4OBC2KGJD243Q5H6A5VOE6Q3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Mixtures of Linear Regressions with Nearly Optimal Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Yingyu Liang, Yuanzhi Li","submitted_at":"2018-02-22T03:47:07Z","abstract_excerpt":"Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated component is also unknown. Previous works either assume strong assumptions on the data distribution or have high complexity. This paper proposes a fixed parameter tractable algorithm for the problem under general conditions, which achieves global convergence and the sample complexity scales nearly linearly in the dimension. In particular, different from previous w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07895","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1802.07895/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:51:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDzXrvslr+WBnG+pmCwWNk/w4tIrxIfTdXAa5LR5b5dbPDrPW1NjoZRdzyFoN7t8PjZsSJzj/7lKXKzCuWGQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T02:29:21.275840Z"},"content_sha256":"ae61bb142345341431cf2a1917252064c351ba56d2903a0ecd89997efab0264e","schema_version":"1.0","event_id":"sha256:ae61bb142345341431cf2a1917252064c351ba56d2903a0ecd89997efab0264e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/bundle.json","state_url":"https://pith.science/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T02:29:21Z","links":{"resolver":"https://pith.science/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I","bundle":"https://pith.science/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/bundle.json","state":"https://pith.science/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C4OBC2KGJD243Q5H6A5VOE6Q3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C4OBC2KGJD243Q5H6A5VOE6Q3I","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":"10a3625797a18b93ef7fe5f2fd267ccf82313357c9de305ef1149530ac5adb57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-22T03:47:07Z","title_canon_sha256":"26397b795c29fd34274272c6264006ceeba66644e4241fa0e48fccc67e7e45e8"},"schema_version":"1.0","source":{"id":"1802.07895","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07895","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07895v3","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07895","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"C4OBC2KGJD24","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_16","alias_value":"C4OBC2KGJD243Q5H","created_at":"2026-07-05T00:51:00Z"},{"alias_kind":"pith_short_8","alias_value":"C4OBC2KG","created_at":"2026-07-05T00:51:00Z"}],"graph_snapshots":[{"event_id":"sha256:ae61bb142345341431cf2a1917252064c351ba56d2903a0ecd89997efab0264e","target":"graph","created_at":"2026-07-05T00:51:00Z","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/1802.07895/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated component is also unknown. Previous works either assume strong assumptions on the data distribution or have high complexity. This paper proposes a fixed parameter tractable algorithm for the problem under general conditions, which achieves global convergence and the sample complexity scales nearly linearly in the dimension. In particular, different from previous w","authors_text":"Yingyu Liang, Yuanzhi Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-22T03:47:07Z","title":"Learning Mixtures of Linear Regressions with Nearly Optimal Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07895","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:fa40776ee635e1e1ec64fafd6a9d9151ea8350f1e248d9bb97d347de49d3408d","target":"record","created_at":"2026-07-05T00:51:00Z","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":"10a3625797a18b93ef7fe5f2fd267ccf82313357c9de305ef1149530ac5adb57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-22T03:47:07Z","title_canon_sha256":"26397b795c29fd34274272c6264006ceeba66644e4241fa0e48fccc67e7e45e8"},"schema_version":"1.0","source":{"id":"1802.07895","kind":"arxiv","version":3}},"canonical_sha256":"171c11694648f5cdc3a7f03b5713d0da1585f9f13738c49fa28992a79c64f311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"171c11694648f5cdc3a7f03b5713d0da1585f9f13738c49fa28992a79c64f311","first_computed_at":"2026-07-05T00:51:00.492119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:51:00.492119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xBoQ3XAF/WXzmM7xNMaxJLfEAdKVN/tDZ2E3U/D0lfVN5UD3XXYhDB2jD9Zh1IYePjdiyt6CXFGyxTDbcAlAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:51:00.492578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07895","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa40776ee635e1e1ec64fafd6a9d9151ea8350f1e248d9bb97d347de49d3408d","sha256:ae61bb142345341431cf2a1917252064c351ba56d2903a0ecd89997efab0264e"],"state_sha256":"000ad1f6bd54f9ccafb0c737ce7b24fb667f5df469008430dfeb69419e37dcb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwHxvpi+uWoEkaiGuGWY0QmK+Wn46lZPrAF91FTDRctorQgIQOdlKmocFvdQDASTGXsZFQELunffyS4x/o19DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T02:29:21.280996Z","bundle_sha256":"26b6e13c97a75e7a0e905cc7f4fdea23145bbb03ba86bf3ed191dac822355626"}}