{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LCWTNJK3AF6UE5IAVHVHH6YMD4","short_pith_number":"pith:LCWTNJK3","canonical_record":{"source":{"id":"1510.08956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-10-30T03:06:00Z","cross_cats_sorted":["cs.LG","stat.ME"],"title_canon_sha256":"7d705106365ef7fe124275e1aeb7006dbed2e99475af732c2f67d626775ae35e","abstract_canon_sha256":"f79f260cda629b6bfa22a78e32ebd4f5cb58fb6c1754683300ca9ecb17605626"},"schema_version":"1.0"},"canonical_sha256":"58ad36a55b017d427500a9ea73fb0c1f37a3ff3198356e1183ddd354028bef6d","source":{"kind":"arxiv","id":"1510.08956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08956","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08956v1","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08956","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"LCWTNJK3AF6U","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LCWTNJK3AF6UE5IA","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LCWTNJK3","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LCWTNJK3AF6UE5IAVHVHH6YMD4","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-10-30T03:06:00Z","cross_cats_sorted":["cs.LG","stat.ME"],"title_canon_sha256":"7d705106365ef7fe124275e1aeb7006dbed2e99475af732c2f67d626775ae35e","abstract_canon_sha256":"f79f260cda629b6bfa22a78e32ebd4f5cb58fb6c1754683300ca9ecb17605626"},"schema_version":"1.0"},"canonical_sha256":"58ad36a55b017d427500a9ea73fb0c1f37a3ff3198356e1183ddd354028bef6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:16.450341Z","signature_b64":"csmlfS9vhCbZzD1eLXtNrlpSVz0YCXWv2tmbTc0u3acv9LUwQ3PnYtlMFob8rZCxh2AUR4bRfTTAN65I+TzjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58ad36a55b017d427500a9ea73fb0c1f37a3ff3198356e1183ddd354028bef6d","last_reissued_at":"2026-05-18T00:45:16.449672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:16.449672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08956","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":"2026-05-18T00:45:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8IECmyAP6brHGeoDC0aS090mwxn2KnKLq+S5AniuItAY3F3+/GoGL2u3ZSJfsDNDaV1U8L8kcVgJJAYgn45Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:22:26.738573Z"},"content_sha256":"715d59a5631cb7173e7662c9f449e3a94075e3860ca8821b6fadf51ec2fdfae6","schema_version":"1.0","event_id":"sha256:715d59a5631cb7173e7662c9f449e3a94075e3860ca8821b6fadf51ec2fdfae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LCWTNJK3AF6UE5IAVHVHH6YMD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Principal Differences Analysis: Interpretable Characterization of Differences between Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ME"],"primary_cat":"stat.ML","authors_text":"Jonas Mueller, Tommi Jaakkola","submitted_at":"2015-10-30T03:06:00Z","abstract_excerpt":"We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08956","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":"2026-05-18T00:45:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQPk9ofeoWDHT4F6jkOhTGxFvKYEbOtUAkU7R7Fo8GzEo3ic+HAw98Ub+0ALif9i5Xe3dRwuWmUGv5Dfzql8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:22:26.739232Z"},"content_sha256":"3a9834c76a867cd203bece5d52d6fb1932e3fb7c71eae3b0909e4a8dbcb1aae3","schema_version":"1.0","event_id":"sha256:3a9834c76a867cd203bece5d52d6fb1932e3fb7c71eae3b0909e4a8dbcb1aae3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/bundle.json","state_url":"https://pith.science/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/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":"2026-05-28T17:22:26Z","links":{"resolver":"https://pith.science/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4","bundle":"https://pith.science/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/bundle.json","state":"https://pith.science/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCWTNJK3AF6UE5IAVHVHH6YMD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LCWTNJK3AF6UE5IAVHVHH6YMD4","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":"f79f260cda629b6bfa22a78e32ebd4f5cb58fb6c1754683300ca9ecb17605626","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-10-30T03:06:00Z","title_canon_sha256":"7d705106365ef7fe124275e1aeb7006dbed2e99475af732c2f67d626775ae35e"},"schema_version":"1.0","source":{"id":"1510.08956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08956","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08956v1","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08956","created_at":"2026-05-18T00:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"LCWTNJK3AF6U","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LCWTNJK3AF6UE5IA","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LCWTNJK3","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:3a9834c76a867cd203bece5d52d6fb1932e3fb7c71eae3b0909e4a8dbcb1aae3","target":"graph","created_at":"2026-05-18T00:45:16Z","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 introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite ","authors_text":"Jonas Mueller, Tommi Jaakkola","cross_cats":["cs.LG","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-10-30T03:06:00Z","title":"Principal Differences Analysis: Interpretable Characterization of Differences between Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08956","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":"sha256:715d59a5631cb7173e7662c9f449e3a94075e3860ca8821b6fadf51ec2fdfae6","target":"record","created_at":"2026-05-18T00:45:16Z","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":"f79f260cda629b6bfa22a78e32ebd4f5cb58fb6c1754683300ca9ecb17605626","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-10-30T03:06:00Z","title_canon_sha256":"7d705106365ef7fe124275e1aeb7006dbed2e99475af732c2f67d626775ae35e"},"schema_version":"1.0","source":{"id":"1510.08956","kind":"arxiv","version":1}},"canonical_sha256":"58ad36a55b017d427500a9ea73fb0c1f37a3ff3198356e1183ddd354028bef6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58ad36a55b017d427500a9ea73fb0c1f37a3ff3198356e1183ddd354028bef6d","first_computed_at":"2026-05-18T00:45:16.449672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:16.449672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csmlfS9vhCbZzD1eLXtNrlpSVz0YCXWv2tmbTc0u3acv9LUwQ3PnYtlMFob8rZCxh2AUR4bRfTTAN65I+TzjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:16.450341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:715d59a5631cb7173e7662c9f449e3a94075e3860ca8821b6fadf51ec2fdfae6","sha256:3a9834c76a867cd203bece5d52d6fb1932e3fb7c71eae3b0909e4a8dbcb1aae3"],"state_sha256":"f504feefacc61687bc06cad72a31016ddb49caff822e69500984dae005eb3ac4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ML1CFsfHOeFAzy5Zsnb7YyP0wZjjEfkeJ53A4Nun2e19NvJiTBm4WFaG/U3T9Qxpx2kaq4oIQrsNeGtE9gTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:22:26.742821Z","bundle_sha256":"f9c600632fdb93f631044dff602bd48b14f263f6da4056791c9642c88e8c313d"}}