{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QXNAPDEFRXTDAG5RRIMFVDTYXU","short_pith_number":"pith:QXNAPDEF","canonical_record":{"source":{"id":"2212.00700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-01T18:06:35Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"51316a80c4b682a3a162543e0cb754aa0d65103d1229f65fc892b1138e872ad2","abstract_canon_sha256":"13a65e102d8c3cda2e41e907f35a184bd37b67b06a971cfcb367e3f6184d3b6f"},"schema_version":"1.0"},"canonical_sha256":"85da078c858de6301bb18a185a8e78bd1432315628a45f5245eb6c0e0b8c026a","source":{"kind":"arxiv","id":"2212.00700","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.00700","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"arxiv_version","alias_value":"2212.00700v3","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.00700","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_12","alias_value":"QXNAPDEFRXTD","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_16","alias_value":"QXNAPDEFRXTDAG5R","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_8","alias_value":"QXNAPDEF","created_at":"2026-07-05T05:23:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QXNAPDEFRXTDAG5RRIMFVDTYXU","target":"record","payload":{"canonical_record":{"source":{"id":"2212.00700","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-01T18:06:35Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"51316a80c4b682a3a162543e0cb754aa0d65103d1229f65fc892b1138e872ad2","abstract_canon_sha256":"13a65e102d8c3cda2e41e907f35a184bd37b67b06a971cfcb367e3f6184d3b6f"},"schema_version":"1.0"},"canonical_sha256":"85da078c858de6301bb18a185a8e78bd1432315628a45f5245eb6c0e0b8c026a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:23:34.517888Z","signature_b64":"1QY1Ucm5PR5AsayX0KiBwGkmYBDOT6HG4YN/J1wqyrmK0UrSmcI5iE3/Buk1kVH/jopapUpR5FMRmMe0gEN1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85da078c858de6301bb18a185a8e78bd1432315628a45f5245eb6c0e0b8c026a","last_reissued_at":"2026-07-05T05:23:34.517442Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:23:34.517442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.00700","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":"2026-07-05T05:23:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KU5nfN7q98YgwII1IjR1iIbtUZ0MSvBJCY/b3S7oESuAPY+L1LgvbcJkXdH5NiwABbrtuBxULpfbp+UyPKpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:07:32.172058Z"},"content_sha256":"736fbfc7c2f7324790c6b7253774c2528b0b139a8aa7620dd8e54c9503dc32b4","schema_version":"1.0","event_id":"sha256:736fbfc7c2f7324790c6b7253774c2528b0b139a8aa7620dd8e54c9503dc32b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QXNAPDEFRXTDAG5RRIMFVDTYXU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Hao Liu, Jiahui Cheng, Minshuo Chen, Tuo Zhao, Wenjing Liao","submitted_at":"2022-12-01T18:06:35Z","abstract_excerpt":"Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.00700","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/2212.00700/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":"2026-07-05T05:23:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7ZYMoaF1neM594ONRrXVPforNq8Y3h9o5MAeKQG1+GcF1T7VbC7mzMfiK+0whqUxeThVzoWxg/gPwF+jS24AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:07:32.172432Z"},"content_sha256":"5a634d36ca247887bc2e2f7628e59fa6443252118eeea27440b5c1135fc98451","schema_version":"1.0","event_id":"sha256:5a634d36ca247887bc2e2f7628e59fa6443252118eeea27440b5c1135fc98451"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/bundle.json","state_url":"https://pith.science/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/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":"2026-08-03T17:07:32Z","links":{"resolver":"https://pith.science/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU","bundle":"https://pith.science/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/bundle.json","state":"https://pith.science/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXNAPDEFRXTDAG5RRIMFVDTYXU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QXNAPDEFRXTDAG5RRIMFVDTYXU","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":"13a65e102d8c3cda2e41e907f35a184bd37b67b06a971cfcb367e3f6184d3b6f","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-01T18:06:35Z","title_canon_sha256":"51316a80c4b682a3a162543e0cb754aa0d65103d1229f65fc892b1138e872ad2"},"schema_version":"1.0","source":{"id":"2212.00700","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.00700","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"arxiv_version","alias_value":"2212.00700v3","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.00700","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_12","alias_value":"QXNAPDEFRXTD","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_16","alias_value":"QXNAPDEFRXTDAG5R","created_at":"2026-07-05T05:23:34Z"},{"alias_kind":"pith_short_8","alias_value":"QXNAPDEF","created_at":"2026-07-05T05:23:34Z"}],"graph_snapshots":[{"event_id":"sha256:5a634d36ca247887bc2e2f7628e59fa6443252118eeea27440b5c1135fc98451","target":"graph","created_at":"2026-07-05T05:23:34Z","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/2212.00700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that","authors_text":"Hao Liu, Jiahui Cheng, Minshuo Chen, Tuo Zhao, Wenjing Liao","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-01T18:06:35Z","title":"High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.00700","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":"sha256:736fbfc7c2f7324790c6b7253774c2528b0b139a8aa7620dd8e54c9503dc32b4","target":"record","created_at":"2026-07-05T05:23:34Z","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":"13a65e102d8c3cda2e41e907f35a184bd37b67b06a971cfcb367e3f6184d3b6f","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-12-01T18:06:35Z","title_canon_sha256":"51316a80c4b682a3a162543e0cb754aa0d65103d1229f65fc892b1138e872ad2"},"schema_version":"1.0","source":{"id":"2212.00700","kind":"arxiv","version":3}},"canonical_sha256":"85da078c858de6301bb18a185a8e78bd1432315628a45f5245eb6c0e0b8c026a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85da078c858de6301bb18a185a8e78bd1432315628a45f5245eb6c0e0b8c026a","first_computed_at":"2026-07-05T05:23:34.517442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:23:34.517442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1QY1Ucm5PR5AsayX0KiBwGkmYBDOT6HG4YN/J1wqyrmK0UrSmcI5iE3/Buk1kVH/jopapUpR5FMRmMe0gEN1DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:23:34.517888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.00700","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:736fbfc7c2f7324790c6b7253774c2528b0b139a8aa7620dd8e54c9503dc32b4","sha256:5a634d36ca247887bc2e2f7628e59fa6443252118eeea27440b5c1135fc98451"],"state_sha256":"0252ecc2ea1c790df5ac6f0c745abdeefb733e59c20c37fd9bc1ecfc6401fc87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WKkTC8I+s58F10p0b//ZsIqw6tizNqHxrKU25bmJdBV36ypQIDClXkjUfZPcqQdI6XW8O2L08b+5Ff68W3J+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:07:32.175173Z","bundle_sha256":"4e7b8f7c07b53931bffd58eca892df460191552d136d365b179b310e48574292"}}