{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:UNFPHX4NBJGSYT2ESXKRMUNXYY","short_pith_number":"pith:UNFPHX4N","canonical_record":{"source":{"id":"0902.1284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-02-08T02:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"15b01d7189aa89eab54210fe1472b45293c58cb146e1043a6f1506b89731b483","abstract_canon_sha256":"3cbebcc758624b7d23b33b9daf7182146a962a8014c5fe5db0f66cc369fd8060"},"schema_version":"1.0"},"canonical_sha256":"a34af3df8d0a4d2c4f4495d51651b7c61a03978cd6188a20725d17f5b372c05e","source":{"kind":"arxiv","id":"0902.1284","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1284","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1284v2","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1284","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_12","alias_value":"UNFPHX4NBJGS","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_16","alias_value":"UNFPHX4NBJGSYT2E","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_8","alias_value":"UNFPHX4N","created_at":"2026-07-04T15:43:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:UNFPHX4NBJGSYT2ESXKRMUNXYY","target":"record","payload":{"canonical_record":{"source":{"id":"0902.1284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-02-08T02:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"15b01d7189aa89eab54210fe1472b45293c58cb146e1043a6f1506b89731b483","abstract_canon_sha256":"3cbebcc758624b7d23b33b9daf7182146a962a8014c5fe5db0f66cc369fd8060"},"schema_version":"1.0"},"canonical_sha256":"a34af3df8d0a4d2c4f4495d51651b7c61a03978cd6188a20725d17f5b372c05e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:43:12.271720Z","signature_b64":"0OYUHLqi9CkNoWUH6VyJNQsV8jEPiZkxcrh277Ts23byfUT+VwhZC5pm3AC4Sgk/eQhad5vrZ477fJ2myTDbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a34af3df8d0a4d2c4f4495d51651b7c61a03978cd6188a20725d17f5b372c05e","last_reissued_at":"2026-07-04T15:43:12.271379Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:43:12.271379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.1284","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:43:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CEKr6RUmya6u0BGZif+jQHcVz2TnRmgzlOSB1E7XD5V5F6dB+USMcvReWQgGABN2X7SocFwsxtrnTlq1kplRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:54:09.535745Z"},"content_sha256":"73a4080438ff7808f26d2d3cec7a3ca5e582d03758397209c0ef945c5c5c6a0a","schema_version":"1.0","event_id":"sha256:73a4080438ff7808f26d2d3cec7a3ca5e582d03758397209c0ef945c5c5c6a0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:UNFPHX4NBJGSYT2ESXKRMUNXYY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Label Prediction via Compressed Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Daniel Hsu, John Langford, Sham M. Kakade, Tong Zhang","submitted_at":"2009-02-08T02:30:06Z","abstract_excerpt":"We consider multi-label prediction problems with large output spaces under the assumption of output sparsity -- that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than othe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1284","kind":"arxiv","version":2},"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/0902.1284/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":"2026-07-04T15:43:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"heiY6MaMw51XbRhIklCrD1paNyNOKWzVIfko33umYF8IYZDJKyEaZ0bq1EZ2vSb8t1vxywbQq4sT2sYa0ETQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:54:09.536624Z"},"content_sha256":"a76b41589ae8c77a85adfe8e9da2d3221a63291c27dcb38b821ff3e3e014a6a7","schema_version":"1.0","event_id":"sha256:a76b41589ae8c77a85adfe8e9da2d3221a63291c27dcb38b821ff3e3e014a6a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/bundle.json","state_url":"https://pith.science/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/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":"2026-08-11T02:54:09Z","links":{"resolver":"https://pith.science/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY","bundle":"https://pith.science/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/bundle.json","state":"https://pith.science/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNFPHX4NBJGSYT2ESXKRMUNXYY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UNFPHX4NBJGSYT2ESXKRMUNXYY","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":"3cbebcc758624b7d23b33b9daf7182146a962a8014c5fe5db0f66cc369fd8060","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-02-08T02:30:06Z","title_canon_sha256":"15b01d7189aa89eab54210fe1472b45293c58cb146e1043a6f1506b89731b483"},"schema_version":"1.0","source":{"id":"0902.1284","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1284","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1284v2","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1284","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_12","alias_value":"UNFPHX4NBJGS","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_16","alias_value":"UNFPHX4NBJGSYT2E","created_at":"2026-07-04T15:43:12Z"},{"alias_kind":"pith_short_8","alias_value":"UNFPHX4N","created_at":"2026-07-04T15:43:12Z"}],"graph_snapshots":[{"event_id":"sha256:a76b41589ae8c77a85adfe8e9da2d3221a63291c27dcb38b821ff3e3e014a6a7","target":"graph","created_at":"2026-07-04T15:43:12Z","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/0902.1284/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider multi-label prediction problems with large output spaces under the assumption of output sparsity -- that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than othe","authors_text":"Daniel Hsu, John Langford, Sham M. Kakade, Tong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-02-08T02:30:06Z","title":"Multi-Label Prediction via Compressed Sensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1284","kind":"arxiv","version":2},"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":"sha256:73a4080438ff7808f26d2d3cec7a3ca5e582d03758397209c0ef945c5c5c6a0a","target":"record","created_at":"2026-07-04T15:43:12Z","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":"3cbebcc758624b7d23b33b9daf7182146a962a8014c5fe5db0f66cc369fd8060","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-02-08T02:30:06Z","title_canon_sha256":"15b01d7189aa89eab54210fe1472b45293c58cb146e1043a6f1506b89731b483"},"schema_version":"1.0","source":{"id":"0902.1284","kind":"arxiv","version":2}},"canonical_sha256":"a34af3df8d0a4d2c4f4495d51651b7c61a03978cd6188a20725d17f5b372c05e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a34af3df8d0a4d2c4f4495d51651b7c61a03978cd6188a20725d17f5b372c05e","first_computed_at":"2026-07-04T15:43:12.271379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:43:12.271379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OYUHLqi9CkNoWUH6VyJNQsV8jEPiZkxcrh277Ts23byfUT+VwhZC5pm3AC4Sgk/eQhad5vrZ477fJ2myTDbDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:43:12.271720Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1284","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a4080438ff7808f26d2d3cec7a3ca5e582d03758397209c0ef945c5c5c6a0a","sha256:a76b41589ae8c77a85adfe8e9da2d3221a63291c27dcb38b821ff3e3e014a6a7"],"state_sha256":"0699f25ee3a0ebff56da1344f821f62b8d6f2d2e5fd9a9719f65c8f89d993957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vla21eNrBjfWyX28G+07qcLSAwLJ9SU2LbpbEb8u7cMmZO/pyo0wdA4Yi3ZQSBoaaGwxfdBrrY48v+6KXLKGDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T02:54:09.543465Z","bundle_sha256":"479b01b913cfd3b60ab00aeb2474764533aac3cf01c7c5c2306629d3da680aa0"}}