{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AC4KTHSPG3GFAFVPNOC3XMECPS","short_pith_number":"pith:AC4KTHSP","canonical_record":{"source":{"id":"1410.3561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-14T03:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"e525703c936b960783b777e92f9ccce51dec8de484521a4661af20cae6692017","abstract_canon_sha256":"d47ff402c18b40b390ccbb2c0ec0d5e5ad4f247c489e2ea6ed4ecc3cd17eda54"},"schema_version":"1.0"},"canonical_sha256":"00b8a99e4f36cc5016af6b85bbb0827c9ab5e7dc0a4f3ecd7baf2c431b0e4247","source":{"kind":"arxiv","id":"1410.3561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3561","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3561v1","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3561","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"AC4KTHSPG3GF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AC4KTHSPG3GFAFVP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AC4KTHSP","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AC4KTHSPG3GFAFVPNOC3XMECPS","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-14T03:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"e525703c936b960783b777e92f9ccce51dec8de484521a4661af20cae6692017","abstract_canon_sha256":"d47ff402c18b40b390ccbb2c0ec0d5e5ad4f247c489e2ea6ed4ecc3cd17eda54"},"schema_version":"1.0"},"canonical_sha256":"00b8a99e4f36cc5016af6b85bbb0827c9ab5e7dc0a4f3ecd7baf2c431b0e4247","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:09.515806Z","signature_b64":"Bikmk08lM6QuhG4ROacfTZckbo/752edS++5HvC9SadzMjMDDYXAnRJewmLswKX34m/+NgRc+0xKvkae/3Q6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00b8a99e4f36cc5016af6b85bbb0827c9ab5e7dc0a4f3ecd7baf2c431b0e4247","last_reissued_at":"2026-05-18T02:40:09.515273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:09.515273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3561","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EWFifAAWivhqzZ7TRh4B2nT7tIVXZRZ+jpedfRTaS3cZtx2mkHvZhh5MgmrYEARR2LSjacRXZsIjfgvV4W/lAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:52:50.440651Z"},"content_sha256":"af7671ed4dc53bb2b2edf71072ea48cc76280b53b1326b809a68214920ead0a5","schema_version":"1.0","event_id":"sha256:af7671ed4dc53bb2b2edf71072ea48cc76280b53b1326b809a68214920ead0a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AC4KTHSPG3GFAFVPNOC3XMECPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sufficient dimension reduction with additional information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Chih-Yen Liu, Henry Horng-Shing Lu, Hung Hung","submitted_at":"2014-10-14T03:44:35Z","abstract_excerpt":"Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable $W$ that is strongly correlated with $Y$. From a statistical point of view, making inference about $(Y,X)$ without using $W$ will lose efficiency. However, it is not trivial to incorporate the information of $W$ to infer $(Y,X)$. In this article, we propose a two-stage dimension reduction method for $(Y,X)$, that is able to utilize the additional information "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3561","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+9CgnxKLH2wMiCIvzNDAp3fYs9OW5byutPQKfAZKNrzrwWbvYNK4ItkZoKHipuG8d1ObvFNc8ajzLaljQQ3kCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:52:50.440991Z"},"content_sha256":"01bfeb60b6547c5e1ea7cd139c3b548f5afb053ed3179099aaccd626a771a8fe","schema_version":"1.0","event_id":"sha256:01bfeb60b6547c5e1ea7cd139c3b548f5afb053ed3179099aaccd626a771a8fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/bundle.json","state_url":"https://pith.science/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/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":"2026-06-21T08:52:50Z","links":{"resolver":"https://pith.science/pith/AC4KTHSPG3GFAFVPNOC3XMECPS","bundle":"https://pith.science/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/bundle.json","state":"https://pith.science/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AC4KTHSPG3GFAFVPNOC3XMECPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AC4KTHSPG3GFAFVPNOC3XMECPS","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":"d47ff402c18b40b390ccbb2c0ec0d5e5ad4f247c489e2ea6ed4ecc3cd17eda54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-14T03:44:35Z","title_canon_sha256":"e525703c936b960783b777e92f9ccce51dec8de484521a4661af20cae6692017"},"schema_version":"1.0","source":{"id":"1410.3561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3561","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3561v1","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3561","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"AC4KTHSPG3GF","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AC4KTHSPG3GFAFVP","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AC4KTHSP","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:01bfeb60b6547c5e1ea7cd139c3b548f5afb053ed3179099aaccd626a771a8fe","target":"graph","created_at":"2026-05-18T02:40:09Z","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"},"paper":{"abstract_excerpt":"Sufficient dimension reduction is widely applied to help model building between the response $Y$ and covariate $X$. While the target of interest is the relationship between $(Y,X)$, in some applications we also collect additional variable $W$ that is strongly correlated with $Y$. From a statistical point of view, making inference about $(Y,X)$ without using $W$ will lose efficiency. However, it is not trivial to incorporate the information of $W$ to infer $(Y,X)$. In this article, we propose a two-stage dimension reduction method for $(Y,X)$, that is able to utilize the additional information ","authors_text":"Chih-Yen Liu, Henry Horng-Shing Lu, Hung Hung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-14T03:44:35Z","title":"Sufficient dimension reduction with additional information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3561","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:af7671ed4dc53bb2b2edf71072ea48cc76280b53b1326b809a68214920ead0a5","target":"record","created_at":"2026-05-18T02:40:09Z","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":"d47ff402c18b40b390ccbb2c0ec0d5e5ad4f247c489e2ea6ed4ecc3cd17eda54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-10-14T03:44:35Z","title_canon_sha256":"e525703c936b960783b777e92f9ccce51dec8de484521a4661af20cae6692017"},"schema_version":"1.0","source":{"id":"1410.3561","kind":"arxiv","version":1}},"canonical_sha256":"00b8a99e4f36cc5016af6b85bbb0827c9ab5e7dc0a4f3ecd7baf2c431b0e4247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00b8a99e4f36cc5016af6b85bbb0827c9ab5e7dc0a4f3ecd7baf2c431b0e4247","first_computed_at":"2026-05-18T02:40:09.515273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:09.515273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bikmk08lM6QuhG4ROacfTZckbo/752edS++5HvC9SadzMjMDDYXAnRJewmLswKX34m/+NgRc+0xKvkae/3Q6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:09.515806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af7671ed4dc53bb2b2edf71072ea48cc76280b53b1326b809a68214920ead0a5","sha256:01bfeb60b6547c5e1ea7cd139c3b548f5afb053ed3179099aaccd626a771a8fe"],"state_sha256":"9025c8722c2c4c456b791d4d9398686e69e12557ac3a22c7c124b3e4066e1c66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2F2MKoMowE+gsrJl705s7xbhmWlyvYJmukmEu3c9/PdiXqwSKEgYDhIXfj/u3swb1g7wtgGZr6QRu4u/CCgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:52:50.442871Z","bundle_sha256":"0a2e1621c6ee65a8daf561875bc8c1585c62aac3d8738ee44fd8e62d55b9a333"}}