{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VJTWTJHCZC7I7BTAPIUYHOOAUT","short_pith_number":"pith:VJTWTJHC","schema_version":"1.0","canonical_sha256":"aa6769a4e2c8be8f86607a2983b9c0a4d5f70b560cec2815c0fd6ed0c65f066f","source":{"kind":"arxiv","id":"1612.00374","version":2},"attestation_state":"computed","paper":{"title":"Spatial Decompositions for Large Scale SVMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ingo Steinwart, Ingrid Blaschzyk, Mona Meister, Philipp Thomann","submitted_at":"2016-12-01T18:14:33Z","abstract_excerpt":"Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several approaches have been proposed in the past to address this serious limitation. In this work we investigate a decomposition strategy that learns on small, spatially defined data chunks. Our contributions are two fold: On the theoretical side we establish an oracle inequality for the overall learning method using the hinge loss, and show that the resulting rates mat"},"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":"1612.00374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-01T18:14:33Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"45183c8dd274330f63b7056b107527be9604d03946afdda4533daeaa8bc2a8e6","abstract_canon_sha256":"bea95844539856e360dc830b89fda7b1f40e2b9b80af873265b5b5bd1d2d5e16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:04.564794Z","signature_b64":"yQKSjF3f7CTKsv6VssXqlKzL+scHxxJaAnWNKY64stcVwvs7eIpHVQQ8H0cZkhAduJAXUPyqBOD7sg2HJVW6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa6769a4e2c8be8f86607a2983b9c0a4d5f70b560cec2815c0fd6ed0c65f066f","last_reissued_at":"2026-05-18T00:24:04.564321Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:04.564321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spatial Decompositions for Large Scale SVMs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Ingo Steinwart, Ingrid Blaschzyk, Mona Meister, Philipp Thomann","submitted_at":"2016-12-01T18:14:33Z","abstract_excerpt":"Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several approaches have been proposed in the past to address this serious limitation. In this work we investigate a decomposition strategy that learns on small, spatially defined data chunks. Our contributions are two fold: On the theoretical side we establish an oracle inequality for the overall learning method using the hinge loss, and show that the resulting rates mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00374","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.00374","created_at":"2026-05-18T00:24:04.564390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.00374v2","created_at":"2026-05-18T00:24:04.564390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00374","created_at":"2026-05-18T00:24:04.564390+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJTWTJHCZC7I","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJTWTJHCZC7I7BTA","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJTWTJHC","created_at":"2026-05-18T12:30:48.956258+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/VJTWTJHCZC7I7BTAPIUYHOOAUT","json":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT.json","graph_json":"https://pith.science/api/pith-number/VJTWTJHCZC7I7BTAPIUYHOOAUT/graph.json","events_json":"https://pith.science/api/pith-number/VJTWTJHCZC7I7BTAPIUYHOOAUT/events.json","paper":"https://pith.science/paper/VJTWTJHC"},"agent_actions":{"view_html":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT","download_json":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT.json","view_paper":"https://pith.science/paper/VJTWTJHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.00374&json=true","fetch_graph":"https://pith.science/api/pith-number/VJTWTJHCZC7I7BTAPIUYHOOAUT/graph.json","fetch_events":"https://pith.science/api/pith-number/VJTWTJHCZC7I7BTAPIUYHOOAUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT/action/storage_attestation","attest_author":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT/action/author_attestation","sign_citation":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT/action/citation_signature","submit_replication":"https://pith.science/pith/VJTWTJHCZC7I7BTAPIUYHOOAUT/action/replication_record"}},"created_at":"2026-05-18T00:24:04.564390+00:00","updated_at":"2026-05-18T00:24:04.564390+00:00"}