{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LDXATYL3UVLJOC6PAZ2KQWBY7K","short_pith_number":"pith:LDXATYL3","schema_version":"1.0","canonical_sha256":"58ee09e17ba556970bcf0674a85838fab096616e92f1a802c0e079123a8f7dab","source":{"kind":"arxiv","id":"1801.07083","version":1},"attestation_state":"computed","paper":{"title":"Differential Message Importance Measure: A New Approach to the Required Sampling Number in Big Data Structure Characterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Pingyi Fan, Rui She, Shanyun Liu","submitted_at":"2018-01-22T13:38:29Z","abstract_excerpt":"Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process by taking message importance into account, and gives a distribution-free criterion to determine how many samples are required in big data structure characterization. Similar to differential entropy, we define differential message importance measure (DMIM) as a measure of message importance for continuous random variable. The DMIM for many common densities i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.07083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-01-22T13:38:29Z","cross_cats_sorted":["cs.NA","math.IT","math.PR","math.ST","stat.TH"],"title_canon_sha256":"90a6a08c4a3f24897ddc6832c96bd4e604304423f1f55f9468d4ff57f9dc3df2","abstract_canon_sha256":"b63bdf5569adfb465aa49bfa19cf186ef39f12e1afc73ddf45dd842d46413296"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:22.320461Z","signature_b64":"DN8Nh50PkBshddYXLCRSPanEBIuV7iDeyeQqVogfN02EOWMeBAm/juPk3JkNwxnaSG7P49WjC1kTt+UApgsGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58ee09e17ba556970bcf0674a85838fab096616e92f1a802c0e079123a8f7dab","last_reissued_at":"2026-05-18T00:25:22.319958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:22.319958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential Message Importance Measure: A New Approach to the Required Sampling Number in Big Data Structure Characterization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Pingyi Fan, Rui She, Shanyun Liu","submitted_at":"2018-01-22T13:38:29Z","abstract_excerpt":"Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process by taking message importance into account, and gives a distribution-free criterion to determine how many samples are required in big data structure characterization. Similar to differential entropy, we define differential message importance measure (DMIM) as a measure of message importance for continuous random variable. The DMIM for many common densities i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07083","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1801.07083","created_at":"2026-05-18T00:25:22.320034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07083v1","created_at":"2026-05-18T00:25:22.320034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07083","created_at":"2026-05-18T00:25:22.320034+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDXATYL3UVLJ","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDXATYL3UVLJOC6P","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDXATYL3","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K","json":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K.json","graph_json":"https://pith.science/api/pith-number/LDXATYL3UVLJOC6PAZ2KQWBY7K/graph.json","events_json":"https://pith.science/api/pith-number/LDXATYL3UVLJOC6PAZ2KQWBY7K/events.json","paper":"https://pith.science/paper/LDXATYL3"},"agent_actions":{"view_html":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K","download_json":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K.json","view_paper":"https://pith.science/paper/LDXATYL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07083&json=true","fetch_graph":"https://pith.science/api/pith-number/LDXATYL3UVLJOC6PAZ2KQWBY7K/graph.json","fetch_events":"https://pith.science/api/pith-number/LDXATYL3UVLJOC6PAZ2KQWBY7K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K/action/storage_attestation","attest_author":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K/action/author_attestation","sign_citation":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K/action/citation_signature","submit_replication":"https://pith.science/pith/LDXATYL3UVLJOC6PAZ2KQWBY7K/action/replication_record"}},"created_at":"2026-05-18T00:25:22.320034+00:00","updated_at":"2026-05-18T00:25:22.320034+00:00"}