{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JPD3LJUVCITIS6BYHIRUADGP6U","short_pith_number":"pith:JPD3LJUV","canonical_record":{"source":{"id":"1202.1436","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-07T14:38:36Z","cross_cats_sorted":["stat.OT"],"title_canon_sha256":"7182fb075fa5c9f488300d669035d9b1787ff0e3abd2fc298441174a9f2af1ff","abstract_canon_sha256":"3ede7ccda4bf003ae1024f70c4e1db0ecc8245b2ce89f0e97acb54a688f59ad8"},"schema_version":"1.0"},"canonical_sha256":"4bc7b5a69512268978383a23400ccff51d05081455f1a27fbd8375d78be19aea","source":{"kind":"arxiv","id":"1202.1436","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1436","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1436v2","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1436","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"JPD3LJUVCITI","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JPD3LJUVCITIS6BY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JPD3LJUV","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JPD3LJUVCITIS6BYHIRUADGP6U","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1436","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-07T14:38:36Z","cross_cats_sorted":["stat.OT"],"title_canon_sha256":"7182fb075fa5c9f488300d669035d9b1787ff0e3abd2fc298441174a9f2af1ff","abstract_canon_sha256":"3ede7ccda4bf003ae1024f70c4e1db0ecc8245b2ce89f0e97acb54a688f59ad8"},"schema_version":"1.0"},"canonical_sha256":"4bc7b5a69512268978383a23400ccff51d05081455f1a27fbd8375d78be19aea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:01.241045Z","signature_b64":"a0f5gFrMF1b/UVpJG/XqkfmRbNFkyegHA5KjxlL60VxNoPHw/A1CeLosyjk21SAuQe90dJWIKSPCQNudQ1j1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc7b5a69512268978383a23400ccff51d05081455f1a27fbd8375d78be19aea","last_reissued_at":"2026-05-18T01:16:01.240405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:01.240405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1436","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":"2026-05-18T01:16:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlZ1k3qBUYM9ldr7iTsJXvYI/kr0dnNzsCuHo698cDcPT72nwPNu2Z0vwJCslp4umg8A/qKSN2mvA6ob1BFTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:56:58.979168Z"},"content_sha256":"1871e0e06c9aebede61e81487354c1d593e437a202201f973134ee4b896a8c6c","schema_version":"1.0","event_id":"sha256:1871e0e06c9aebede61e81487354c1d593e437a202201f973134ee4b896a8c6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JPD3LJUVCITIS6BYHIRUADGP6U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.OT"],"primary_cat":"stat.ME","authors_text":"Antonio Irpino, Rosanna Verde","submitted_at":"2012-02-07T14:38:36Z","abstract_excerpt":"In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are estimated using the classic Least Squares method. An appropriate metric is introduced in order to measure the error between the observed and the predicted distributions. In particular, the Wasserstein distance is proposed. Some properties of such metric are exploited to predict the response variable as direct linear combination of other independent histogram var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1436","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":"2026-05-18T01:16:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLSGC9rdEKHL1I8oUqhQ6qChD/ABW6BKAg+CEKNiAcey5aCIX9fVHovWrGw7vawHP5s3r6gNewjhzsqrgg08AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:56:58.979569Z"},"content_sha256":"f90c5057af56c61fc376f30172645eee8848b5f6edcd48dfca7c52d77f1fb9c9","schema_version":"1.0","event_id":"sha256:f90c5057af56c61fc376f30172645eee8848b5f6edcd48dfca7c52d77f1fb9c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPD3LJUVCITIS6BYHIRUADGP6U/bundle.json","state_url":"https://pith.science/pith/JPD3LJUVCITIS6BYHIRUADGP6U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPD3LJUVCITIS6BYHIRUADGP6U/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":"2026-06-29T11:56:58Z","links":{"resolver":"https://pith.science/pith/JPD3LJUVCITIS6BYHIRUADGP6U","bundle":"https://pith.science/pith/JPD3LJUVCITIS6BYHIRUADGP6U/bundle.json","state":"https://pith.science/pith/JPD3LJUVCITIS6BYHIRUADGP6U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPD3LJUVCITIS6BYHIRUADGP6U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JPD3LJUVCITIS6BYHIRUADGP6U","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":"3ede7ccda4bf003ae1024f70c4e1db0ecc8245b2ce89f0e97acb54a688f59ad8","cross_cats_sorted":["stat.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-07T14:38:36Z","title_canon_sha256":"7182fb075fa5c9f488300d669035d9b1787ff0e3abd2fc298441174a9f2af1ff"},"schema_version":"1.0","source":{"id":"1202.1436","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1436","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1436v2","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1436","created_at":"2026-05-18T01:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"JPD3LJUVCITI","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JPD3LJUVCITIS6BY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JPD3LJUV","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f90c5057af56c61fc376f30172645eee8848b5f6edcd48dfca7c52d77f1fb9c9","target":"graph","created_at":"2026-05-18T01:16:01Z","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":"In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are estimated using the classic Least Squares method. An appropriate metric is introduced in order to measure the error between the observed and the predicted distributions. In particular, the Wasserstein distance is proposed. Some properties of such metric are exploited to predict the response variable as direct linear combination of other independent histogram var","authors_text":"Antonio Irpino, Rosanna Verde","cross_cats":["stat.OT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-07T14:38:36Z","title":"Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1436","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":"sha256:1871e0e06c9aebede61e81487354c1d593e437a202201f973134ee4b896a8c6c","target":"record","created_at":"2026-05-18T01:16:01Z","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":"3ede7ccda4bf003ae1024f70c4e1db0ecc8245b2ce89f0e97acb54a688f59ad8","cross_cats_sorted":["stat.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-02-07T14:38:36Z","title_canon_sha256":"7182fb075fa5c9f488300d669035d9b1787ff0e3abd2fc298441174a9f2af1ff"},"schema_version":"1.0","source":{"id":"1202.1436","kind":"arxiv","version":2}},"canonical_sha256":"4bc7b5a69512268978383a23400ccff51d05081455f1a27fbd8375d78be19aea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bc7b5a69512268978383a23400ccff51d05081455f1a27fbd8375d78be19aea","first_computed_at":"2026-05-18T01:16:01.240405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:01.240405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a0f5gFrMF1b/UVpJG/XqkfmRbNFkyegHA5KjxlL60VxNoPHw/A1CeLosyjk21SAuQe90dJWIKSPCQNudQ1j1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:01.241045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1436","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1871e0e06c9aebede61e81487354c1d593e437a202201f973134ee4b896a8c6c","sha256:f90c5057af56c61fc376f30172645eee8848b5f6edcd48dfca7c52d77f1fb9c9"],"state_sha256":"9af5647b8274231fd9360126d249b1ffd07d130cb2f313b2736a3681fe8df59f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cctv+Cafz8yzPBsW2GzPWVn0tBVtOGWzIWLBEOvvJMgMIrsN2wM6X+d203W1Qdf3vLzCIBTA0WKfDEpown0FBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T11:56:58.981414Z","bundle_sha256":"b2da363c7f4ebf294006361305a36ba5d41cbd0cb9fb99003174cecc286c42ed"}}