{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JX4LGE6QXRJUA4JR7UBQYL7EGE","short_pith_number":"pith:JX4LGE6Q","canonical_record":{"source":{"id":"1202.6504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-02-29T10:09:26Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"31208f156057fc428228d6d1176f131ee94a182a7c40c4d50405bd396c9503de","abstract_canon_sha256":"e0af8e460ef9c185f5275093b55cb5857a682587dcb0fa9e1392ad387482a6fa"},"schema_version":"1.0"},"canonical_sha256":"4df8b313d0bc53407131fd030c2fe431180263447c2535306e614a3354821ecf","source":{"kind":"arxiv","id":"1202.6504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6504","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6504v2","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6504","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"JX4LGE6QXRJU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JX4LGE6QXRJUA4JR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JX4LGE6Q","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JX4LGE6QXRJUA4JR7UBQYL7EGE","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-02-29T10:09:26Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"31208f156057fc428228d6d1176f131ee94a182a7c40c4d50405bd396c9503de","abstract_canon_sha256":"e0af8e460ef9c185f5275093b55cb5857a682587dcb0fa9e1392ad387482a6fa"},"schema_version":"1.0"},"canonical_sha256":"4df8b313d0bc53407131fd030c2fe431180263447c2535306e614a3354821ecf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:36.974105Z","signature_b64":"9130On1kNALGnM/pub3tS6ZFSGmBOKo2BXgQRljHnrPCppwV6IDRcizP8qLDseQVE0hvAziIiigeSm+g0L6yBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4df8b313d0bc53407131fd030c2fe431180263447c2535306e614a3354821ecf","last_reissued_at":"2026-05-18T03:36:36.973574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:36.973574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6504","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":"2026-05-18T03:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AQU69EbVBTbGC7a2r2gVbncbZqlzphzyCl/yB9bjS5K1I1tNemkUWQRp6Dj17MBUkn7OqhSIqxdvrAxKRqwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:24:56.274861Z"},"content_sha256":"ad6bc17fef5f666bd2a98298fcd168de76195049ed43db8dad183547f0e270ef","schema_version":"1.0","event_id":"sha256:ad6bc17fef5f666bd2a98298fcd168de76195049ed43db8dad183547f0e270ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JX4LGE6QXRJUA4JR7UBQYL7EGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning from Distributions via Support Measure Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Bernhard Sch\\\"olkopf, Francesco Dinuzzo, Kenji Fukumizu, Krikamol Muandet","submitted_at":"2012-02-29T10:09:26Z","abstract_excerpt":"This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6504","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":""},"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":"2026-05-18T03:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIltgFXqtkma1CqsuAZc08GblU+JmbOxvSqrxYMTSQtdwa0Y32Gye5hRUuYnSvZNgUe8yEh51HvoTD3QBsCuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:24:56.275216Z"},"content_sha256":"f3172679f64892dd3d6de935c98829e19fb468abe0fb50a3a929fc2362c807ed","schema_version":"1.0","event_id":"sha256:f3172679f64892dd3d6de935c98829e19fb468abe0fb50a3a929fc2362c807ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/bundle.json","state_url":"https://pith.science/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/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":"2026-06-08T09:24:56Z","links":{"resolver":"https://pith.science/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE","bundle":"https://pith.science/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/bundle.json","state":"https://pith.science/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JX4LGE6QXRJUA4JR7UBQYL7EGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JX4LGE6QXRJUA4JR7UBQYL7EGE","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":"e0af8e460ef9c185f5275093b55cb5857a682587dcb0fa9e1392ad387482a6fa","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-02-29T10:09:26Z","title_canon_sha256":"31208f156057fc428228d6d1176f131ee94a182a7c40c4d50405bd396c9503de"},"schema_version":"1.0","source":{"id":"1202.6504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6504","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6504v2","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6504","created_at":"2026-05-18T03:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"JX4LGE6QXRJU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JX4LGE6QXRJUA4JR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JX4LGE6Q","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f3172679f64892dd3d6de935c98829e19fb468abe0fb50a3a929fc2362c807ed","target":"graph","created_at":"2026-05-18T03:36:36Z","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":"This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM)","authors_text":"Bernhard Sch\\\"olkopf, Francesco Dinuzzo, Kenji Fukumizu, Krikamol Muandet","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-02-29T10:09:26Z","title":"Learning from Distributions via Support Measure Machines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6504","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:ad6bc17fef5f666bd2a98298fcd168de76195049ed43db8dad183547f0e270ef","target":"record","created_at":"2026-05-18T03:36:36Z","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":"e0af8e460ef9c185f5275093b55cb5857a682587dcb0fa9e1392ad387482a6fa","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-02-29T10:09:26Z","title_canon_sha256":"31208f156057fc428228d6d1176f131ee94a182a7c40c4d50405bd396c9503de"},"schema_version":"1.0","source":{"id":"1202.6504","kind":"arxiv","version":2}},"canonical_sha256":"4df8b313d0bc53407131fd030c2fe431180263447c2535306e614a3354821ecf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4df8b313d0bc53407131fd030c2fe431180263447c2535306e614a3354821ecf","first_computed_at":"2026-05-18T03:36:36.973574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:36.973574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9130On1kNALGnM/pub3tS6ZFSGmBOKo2BXgQRljHnrPCppwV6IDRcizP8qLDseQVE0hvAziIiigeSm+g0L6yBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:36.974105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad6bc17fef5f666bd2a98298fcd168de76195049ed43db8dad183547f0e270ef","sha256:f3172679f64892dd3d6de935c98829e19fb468abe0fb50a3a929fc2362c807ed"],"state_sha256":"e97bb873e5a3fb2426ee6ff4076142ca304204f7b5bc3fd91c293956ee58dfd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8bBKexLWUQX76SzbJiYbnzl2gw1JeoeBfkCvH6q1NuS27jlnmuvPY/tTHCN+pikJ4i9xdaFBSoJeZii1NbiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:24:56.277106Z","bundle_sha256":"ed40c5dbb728c1afc9c17ce22be9c181fbc599910159336de98b7fb552078b4b"}}