{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4KYTAL3K2VR6M5ULREN3VWPFM7","short_pith_number":"pith:4KYTAL3K","schema_version":"1.0","canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","source":{"kind":"arxiv","id":"1504.06026","version":1},"attestation_state":"computed","paper":{"title":"Graphical Fermat's Principle and Triangle-Free Graph Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Han Liu, Junwei Lu","submitted_at":"2015-04-23T02:28:16Z","abstract_excerpt":"We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover "},"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":"1504.06026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-04-23T02:28:16Z","cross_cats_sorted":[],"title_canon_sha256":"ba6550f5131ad7cb998c05031159596faa5ed29299617dc2ea20c717c33428b3","abstract_canon_sha256":"026d43725e8b6897504f551ba777627720e616db606963b2890b4bf018d0158d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:02.851769Z","signature_b64":"g6eZzRB0tl8CbU030/ldAVPuPZiTHqBbopryBUVBvj6LYXhnEEecLDbL6XZHorcZ8L4N0t/dmZyXoCnwgcWuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b1302f6ad563e6768b891bbad9e567ff440e09077ae5e9d9b5be3cef25a23f","last_reissued_at":"2026-05-18T02:18:02.851106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:02.851106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphical Fermat's Principle and Triangle-Free Graph Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Han Liu, Junwei Lu","submitted_at":"2015-04-23T02:28:16Z","abstract_excerpt":"We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06026","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":"1504.06026","created_at":"2026-05-18T02:18:02.851187+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06026v1","created_at":"2026-05-18T02:18:02.851187+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06026","created_at":"2026-05-18T02:18:02.851187+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KYTAL3K2VR6","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KYTAL3K2VR6M5UL","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KYTAL3K","created_at":"2026-05-18T12:29:05.191682+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/4KYTAL3K2VR6M5ULREN3VWPFM7","json":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7.json","graph_json":"https://pith.science/api/pith-number/4KYTAL3K2VR6M5ULREN3VWPFM7/graph.json","events_json":"https://pith.science/api/pith-number/4KYTAL3K2VR6M5ULREN3VWPFM7/events.json","paper":"https://pith.science/paper/4KYTAL3K"},"agent_actions":{"view_html":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7","download_json":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7.json","view_paper":"https://pith.science/paper/4KYTAL3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06026&json=true","fetch_graph":"https://pith.science/api/pith-number/4KYTAL3K2VR6M5ULREN3VWPFM7/graph.json","fetch_events":"https://pith.science/api/pith-number/4KYTAL3K2VR6M5ULREN3VWPFM7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/action/storage_attestation","attest_author":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/action/author_attestation","sign_citation":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/action/citation_signature","submit_replication":"https://pith.science/pith/4KYTAL3K2VR6M5ULREN3VWPFM7/action/replication_record"}},"created_at":"2026-05-18T02:18:02.851187+00:00","updated_at":"2026-05-18T02:18:02.851187+00:00"}