{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I4IXLZNFSADVVWHCCWOBYCJV3G","short_pith_number":"pith:I4IXLZNF","schema_version":"1.0","canonical_sha256":"471175e5a590075ad8e2159c1c0935d9bacb97c1d4ff359b8beca3212692b6df","source":{"kind":"arxiv","id":"1601.08169","version":1},"attestation_state":"computed","paper":{"title":"Kernels for sequentially ordered data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LG","math.ST","stat.ME","stat.TH"],"primary_cat":"stat.ML","authors_text":"Franz J Kir\\'aly, Harald Oberhauser","submitted_at":"2016-01-29T16:06:36Z","abstract_excerpt":"We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a \"sequentialized\" version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are shown to approximate a continuous moment form in a sampling sense.\n  A number of known kernels for sequences arise as \"sequentializations\" of suitable static kernels: string kernels may be obtained as a"},"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":"1601.08169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-01-29T16:06:36Z","cross_cats_sorted":["cs.DM","cs.LG","math.ST","stat.ME","stat.TH"],"title_canon_sha256":"7063486363f3946442edfaff7fcd7915d7691bfe18f5309b61b12081fda5b289","abstract_canon_sha256":"f17fe38c711511305d97bbb45e442fa3942cca39fdf4f9eb297e470a8183e28f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.192190Z","signature_b64":"bQfGE+B2mQBD+8P33kS6S59Dem/egpAG040HPwCe8tIl4B30wuXW2y244p4rn0lWXjPx6K3eq/dzVsPwY7xWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471175e5a590075ad8e2159c1c0935d9bacb97c1d4ff359b8beca3212692b6df","last_reissued_at":"2026-05-18T01:21:40.191723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.191723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kernels for sequentially ordered data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LG","math.ST","stat.ME","stat.TH"],"primary_cat":"stat.ML","authors_text":"Franz J Kir\\'aly, Harald Oberhauser","submitted_at":"2016-01-29T16:06:36Z","abstract_excerpt":"We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a \"sequentialized\" version of any static kernel. The sequential kernels are efficiently computable for discrete sequences and are shown to approximate a continuous moment form in a sampling sense.\n  A number of known kernels for sequences arise as \"sequentializations\" of suitable static kernels: string kernels may be obtained as a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08169","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":"1601.08169","created_at":"2026-05-18T01:21:40.191794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.08169v1","created_at":"2026-05-18T01:21:40.191794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08169","created_at":"2026-05-18T01:21:40.191794+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4IXLZNFSADV","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4IXLZNFSADVVWHC","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4IXLZNF","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.18406","citing_title":"Computational aspects of the Volterra Signature","ref_index":23,"is_internal_anchor":true},{"citing_arxiv_id":"2604.04662","citing_title":"Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G","json":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G.json","graph_json":"https://pith.science/api/pith-number/I4IXLZNFSADVVWHCCWOBYCJV3G/graph.json","events_json":"https://pith.science/api/pith-number/I4IXLZNFSADVVWHCCWOBYCJV3G/events.json","paper":"https://pith.science/paper/I4IXLZNF"},"agent_actions":{"view_html":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G","download_json":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G.json","view_paper":"https://pith.science/paper/I4IXLZNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.08169&json=true","fetch_graph":"https://pith.science/api/pith-number/I4IXLZNFSADVVWHCCWOBYCJV3G/graph.json","fetch_events":"https://pith.science/api/pith-number/I4IXLZNFSADVVWHCCWOBYCJV3G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G/action/storage_attestation","attest_author":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G/action/author_attestation","sign_citation":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G/action/citation_signature","submit_replication":"https://pith.science/pith/I4IXLZNFSADVVWHCCWOBYCJV3G/action/replication_record"}},"created_at":"2026-05-18T01:21:40.191794+00:00","updated_at":"2026-05-18T01:21:40.191794+00:00"}