{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UUWIQCGCO3F3ERIX5GUGN6VDDC","short_pith_number":"pith:UUWIQCGC","canonical_record":{"source":{"id":"1408.2031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:25:07Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bd6b842c3bd19d0a4427e4fcbc7efa5c12f4f45e1be15fd844a7454d6e55e54d","abstract_canon_sha256":"e60e8101c40979bebdc893beee8909f47618c9db1bc14232dc22bf2d96ec92b3"},"schema_version":"1.0"},"canonical_sha256":"a52c8808c276cbb24517e9a866faa318b8296d02ad50b9b72de3a418b89c130d","source":{"kind":"arxiv","id":"1408.2031","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2031","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2031v1","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2031","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"UUWIQCGCO3F3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UUWIQCGCO3F3ERIX","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UUWIQCGC","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UUWIQCGCO3F3ERIX5GUGN6VDDC","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:25:07Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bd6b842c3bd19d0a4427e4fcbc7efa5c12f4f45e1be15fd844a7454d6e55e54d","abstract_canon_sha256":"e60e8101c40979bebdc893beee8909f47618c9db1bc14232dc22bf2d96ec92b3"},"schema_version":"1.0"},"canonical_sha256":"a52c8808c276cbb24517e9a866faa318b8296d02ad50b9b72de3a418b89c130d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:30.676964Z","signature_b64":"5z9Dj58h67M6Q3UpbeFGnyCR1HVJfhudtU/Dv894jWJkfMSpJ9bRTPXeTeuWa+8dpFEhh9ZDrLb2/W0kbceWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a52c8808c276cbb24517e9a866faa318b8296d02ad50b9b72de3a418b89c130d","last_reissued_at":"2026-05-18T02:45:30.676385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:30.676385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2031","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":"2026-05-18T02:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBrccJNYAA0wtQKdKIC385C24TlEWOF5rHX20BYxBXTYunUjSwH0/3DJZcUDANHsf+o6Q11aPP6p+VemKnb9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:39:16.247680Z"},"content_sha256":"94325f227ce2dc1121e19f0ed9ea41bb49e4ba9c4e8771528cc54a1efdec8781","schema_version":"1.0","event_id":"sha256:94325f227ce2dc1121e19f0ed9ea41bb49e4ba9c4e8771528cc54a1efdec8781"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UUWIQCGCO3F3ERIX5GUGN6VDDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional Probability Tree Estimation Analysis and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexander L. Strehl, Alina Beygelzimer, Gregory Sorkin, John Langford, Yuri Lifshits","submitted_at":"2014-08-09T05:25:07Z","abstract_excerpt":"We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly 106 labels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2031","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":"2026-05-18T02:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zqFrhT1dcLWGJVGeBo6iDx02wx3tjpRStcrezBkVUkH9Fcz0Q1wpr9HeLEXmlfz5bvLd6CiwDK/qJ6qyAI6xBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:39:16.248340Z"},"content_sha256":"6625bda19fa4c3de0e0dc4b3cf882791e875e53b071f28791a5c7e27b3326e3e","schema_version":"1.0","event_id":"sha256:6625bda19fa4c3de0e0dc4b3cf882791e875e53b071f28791a5c7e27b3326e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/bundle.json","state_url":"https://pith.science/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/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":"2026-05-26T21:39:16Z","links":{"resolver":"https://pith.science/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC","bundle":"https://pith.science/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/bundle.json","state":"https://pith.science/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUWIQCGCO3F3ERIX5GUGN6VDDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UUWIQCGCO3F3ERIX5GUGN6VDDC","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":"e60e8101c40979bebdc893beee8909f47618c9db1bc14232dc22bf2d96ec92b3","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:25:07Z","title_canon_sha256":"bd6b842c3bd19d0a4427e4fcbc7efa5c12f4f45e1be15fd844a7454d6e55e54d"},"schema_version":"1.0","source":{"id":"1408.2031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2031","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2031v1","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2031","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"UUWIQCGCO3F3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UUWIQCGCO3F3ERIX","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UUWIQCGC","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:6625bda19fa4c3de0e0dc4b3cf882791e875e53b071f28791a5c7e27b3326e3e","target":"graph","created_at":"2026-05-18T02:45:30Z","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":"We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly 106 labels.","authors_text":"Alexander L. Strehl, Alina Beygelzimer, Gregory Sorkin, John Langford, Yuri Lifshits","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:25:07Z","title":"Conditional Probability Tree Estimation Analysis and Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2031","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":"sha256:94325f227ce2dc1121e19f0ed9ea41bb49e4ba9c4e8771528cc54a1efdec8781","target":"record","created_at":"2026-05-18T02:45:30Z","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":"e60e8101c40979bebdc893beee8909f47618c9db1bc14232dc22bf2d96ec92b3","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:25:07Z","title_canon_sha256":"bd6b842c3bd19d0a4427e4fcbc7efa5c12f4f45e1be15fd844a7454d6e55e54d"},"schema_version":"1.0","source":{"id":"1408.2031","kind":"arxiv","version":1}},"canonical_sha256":"a52c8808c276cbb24517e9a866faa318b8296d02ad50b9b72de3a418b89c130d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52c8808c276cbb24517e9a866faa318b8296d02ad50b9b72de3a418b89c130d","first_computed_at":"2026-05-18T02:45:30.676385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:30.676385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5z9Dj58h67M6Q3UpbeFGnyCR1HVJfhudtU/Dv894jWJkfMSpJ9bRTPXeTeuWa+8dpFEhh9ZDrLb2/W0kbceWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:30.676964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94325f227ce2dc1121e19f0ed9ea41bb49e4ba9c4e8771528cc54a1efdec8781","sha256:6625bda19fa4c3de0e0dc4b3cf882791e875e53b071f28791a5c7e27b3326e3e"],"state_sha256":"c24c14032027d1bb01fe3412453d6ec16c470c9a4f0eeee6167380e30700f714"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qc+NtztVGBu8/eIFrMGsmWQNyiAExhRQT9g/U4IkfQv+p0QAk5X9b6nMB0EF6NhOcj9W3HhMf8KPYRLYS91CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:39:16.251621Z","bundle_sha256":"ddcc4c75d56833a1051a4ca2f826fc907472e02b5e0e7cbf7cdc524d547fc87f"}}