{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LD3DXP2EYPXKCKY5NOZO6WWI4K","short_pith_number":"pith:LD3DXP2E","schema_version":"1.0","canonical_sha256":"58f63bbf44c3eea12b1d6bb2ef5ac8e2b8d7f436b4da2a5946183b8932a54bb3","source":{"kind":"arxiv","id":"1609.01176","version":1},"attestation_state":"computed","paper":{"title":"The Player Kernel: Learning Team Strengths Based on Implicit Player Contributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"cs.LG","authors_text":"Antonio J. Gonz\\'alez Ferrer, Lucas Maystre, Matthias Grossglauser, Victor Kristof","submitted_at":"2016-09-05T14:21:04Z","abstract_excerpt":"In this work, we draw attention to a connection between skill-based models of game outcomes and Gaussian process classification models. The Gaussian process perspective enables a) a principled way of dealing with uncertainty and b) rich models, specified through kernel functions. Using this connection, we tackle the problem of predicting outcomes of football matches between national teams. We develop a player kernel that relates any two football matches through the players lined up on the field. This makes it possible to share knowledge gained from observing matches between clubs (available in"},"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":"1609.01176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-09-05T14:21:04Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"9bc20a039323008ab585f58cc0ce207be263aad109bcbf9bc9a2ba1c27fea6c2","abstract_canon_sha256":"c11e98dd51cb7c7f3cab078bfd31f05e7283d216fdd70f61ba68d2eb2c752726"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:18.806306Z","signature_b64":"7bOGRQbMv+7ukvpBOBJCu6mN42EBh2L36vld31QAnPZqcCYFYyYSa42O9zas2hotql4Jzg/FuL3AB5Pklcs6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58f63bbf44c3eea12b1d6bb2ef5ac8e2b8d7f436b4da2a5946183b8932a54bb3","last_reissued_at":"2026-05-18T01:06:18.805647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:18.805647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Player Kernel: Learning Team Strengths Based on Implicit Player Contributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"cs.LG","authors_text":"Antonio J. Gonz\\'alez Ferrer, Lucas Maystre, Matthias Grossglauser, Victor Kristof","submitted_at":"2016-09-05T14:21:04Z","abstract_excerpt":"In this work, we draw attention to a connection between skill-based models of game outcomes and Gaussian process classification models. The Gaussian process perspective enables a) a principled way of dealing with uncertainty and b) rich models, specified through kernel functions. Using this connection, we tackle the problem of predicting outcomes of football matches between national teams. We develop a player kernel that relates any two football matches through the players lined up on the field. This makes it possible to share knowledge gained from observing matches between clubs (available in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01176","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":"1609.01176","created_at":"2026-05-18T01:06:18.805761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01176v1","created_at":"2026-05-18T01:06:18.805761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01176","created_at":"2026-05-18T01:06:18.805761+00:00"},{"alias_kind":"pith_short_12","alias_value":"LD3DXP2EYPXK","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LD3DXP2EYPXKCKY5","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LD3DXP2E","created_at":"2026-05-18T12:30:29.479603+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/LD3DXP2EYPXKCKY5NOZO6WWI4K","json":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K.json","graph_json":"https://pith.science/api/pith-number/LD3DXP2EYPXKCKY5NOZO6WWI4K/graph.json","events_json":"https://pith.science/api/pith-number/LD3DXP2EYPXKCKY5NOZO6WWI4K/events.json","paper":"https://pith.science/paper/LD3DXP2E"},"agent_actions":{"view_html":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K","download_json":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K.json","view_paper":"https://pith.science/paper/LD3DXP2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01176&json=true","fetch_graph":"https://pith.science/api/pith-number/LD3DXP2EYPXKCKY5NOZO6WWI4K/graph.json","fetch_events":"https://pith.science/api/pith-number/LD3DXP2EYPXKCKY5NOZO6WWI4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K/action/storage_attestation","attest_author":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K/action/author_attestation","sign_citation":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K/action/citation_signature","submit_replication":"https://pith.science/pith/LD3DXP2EYPXKCKY5NOZO6WWI4K/action/replication_record"}},"created_at":"2026-05-18T01:06:18.805761+00:00","updated_at":"2026-05-18T01:06:18.805761+00:00"}