{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BC5FQVV7AUPV2GKLHIVGDYJAUC","short_pith_number":"pith:BC5FQVV7","canonical_record":{"source":{"id":"1710.11345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-31T06:44:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a83b30773175277cf20b54ba4245831386b6cbfaf0b5a514e02010a571a4620f","abstract_canon_sha256":"4f903bbd0d6ea64476010d19fafa37e1d4c5b97cb63346bb7571b6747db9e0e6"},"schema_version":"1.0"},"canonical_sha256":"08ba5856bf051f5d194b3a2a61e120a0ba4f98ec809e4da08d161a8f67d9c894","source":{"kind":"arxiv","id":"1710.11345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11345","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11345v1","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11345","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"BC5FQVV7AUPV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BC5FQVV7AUPV2GKL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BC5FQVV7","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BC5FQVV7AUPV2GKLHIVGDYJAUC","target":"record","payload":{"canonical_record":{"source":{"id":"1710.11345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-31T06:44:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a83b30773175277cf20b54ba4245831386b6cbfaf0b5a514e02010a571a4620f","abstract_canon_sha256":"4f903bbd0d6ea64476010d19fafa37e1d4c5b97cb63346bb7571b6747db9e0e6"},"schema_version":"1.0"},"canonical_sha256":"08ba5856bf051f5d194b3a2a61e120a0ba4f98ec809e4da08d161a8f67d9c894","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:44.161745Z","signature_b64":"tTCa+EmC0KEKQZMpME56QI4Yf4ngLoM9S133LDPBN047egppC0D/LpH7Ombruyxiq9FN8C7vROAMujSjp1tmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08ba5856bf051f5d194b3a2a61e120a0ba4f98ec809e4da08d161a8f67d9c894","last_reissued_at":"2026-05-18T00:31:44.160915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:44.160915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.11345","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTzes16ACXiN4fAuYH0wnxaSPnrbSytvxHztppyUtCGMRcGq09wreQLph9q6x3D4RXgCcaulndFQ+tL/1Am4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:49:17.034758Z"},"content_sha256":"8305b9443dbeca50b7ecf5d4bcaace2d7ed2917e70a142f9cb5f0dfff880747c","schema_version":"1.0","event_id":"sha256:8305b9443dbeca50b7ecf5d4bcaace2d7ed2917e70a142f9cb5f0dfff880747c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BC5FQVV7AUPV2GKLHIVGDYJAUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor Regression Meets Gaussian Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Guangyu Li, Rose Yu, Yan Liu","submitted_at":"2017-10-31T06:44:59Z","abstract_excerpt":"Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the ave"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11345","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4aOvqFNoIGqnY1DaVqQnT3Tj96gcKcurBjt5Td6D+849lmv/eeUcMBUwYVyutkW9OhhRrn67aEv/eE3b0fjcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:49:17.035104Z"},"content_sha256":"051d75d201f0b4cc152c8ca528e4ad3721e198f31fd34960204a01b961405dec","schema_version":"1.0","event_id":"sha256:051d75d201f0b4cc152c8ca528e4ad3721e198f31fd34960204a01b961405dec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/bundle.json","state_url":"https://pith.science/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T13:49:17Z","links":{"resolver":"https://pith.science/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC","bundle":"https://pith.science/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/bundle.json","state":"https://pith.science/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BC5FQVV7AUPV2GKLHIVGDYJAUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BC5FQVV7AUPV2GKLHIVGDYJAUC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4f903bbd0d6ea64476010d19fafa37e1d4c5b97cb63346bb7571b6747db9e0e6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-31T06:44:59Z","title_canon_sha256":"a83b30773175277cf20b54ba4245831386b6cbfaf0b5a514e02010a571a4620f"},"schema_version":"1.0","source":{"id":"1710.11345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11345","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11345v1","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11345","created_at":"2026-05-18T00:31:44Z"},{"alias_kind":"pith_short_12","alias_value":"BC5FQVV7AUPV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BC5FQVV7AUPV2GKL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BC5FQVV7","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:051d75d201f0b4cc152c8ca528e4ad3721e198f31fd34960204a01b961405dec","target":"graph","created_at":"2026-05-18T00:31:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the ave","authors_text":"Guangyu Li, Rose Yu, Yan Liu","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-31T06:44:59Z","title":"Tensor Regression Meets Gaussian Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11345","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8305b9443dbeca50b7ecf5d4bcaace2d7ed2917e70a142f9cb5f0dfff880747c","target":"record","created_at":"2026-05-18T00:31:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4f903bbd0d6ea64476010d19fafa37e1d4c5b97cb63346bb7571b6747db9e0e6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-10-31T06:44:59Z","title_canon_sha256":"a83b30773175277cf20b54ba4245831386b6cbfaf0b5a514e02010a571a4620f"},"schema_version":"1.0","source":{"id":"1710.11345","kind":"arxiv","version":1}},"canonical_sha256":"08ba5856bf051f5d194b3a2a61e120a0ba4f98ec809e4da08d161a8f67d9c894","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08ba5856bf051f5d194b3a2a61e120a0ba4f98ec809e4da08d161a8f67d9c894","first_computed_at":"2026-05-18T00:31:44.160915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:44.160915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tTCa+EmC0KEKQZMpME56QI4Yf4ngLoM9S133LDPBN047egppC0D/LpH7Ombruyxiq9FN8C7vROAMujSjp1tmCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:44.161745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8305b9443dbeca50b7ecf5d4bcaace2d7ed2917e70a142f9cb5f0dfff880747c","sha256:051d75d201f0b4cc152c8ca528e4ad3721e198f31fd34960204a01b961405dec"],"state_sha256":"b2da22673dca4231bcb33f548d1f68836be978802f8fee300eed442997eba686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3nZpNeD3wGQUDZrZjAt4+7rTtmdmdl0r/zTQZeCtI9rfACtzRr55D9mAb8HguJmMyZ+83QSiJeGBm1QEdaaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:49:17.037052Z","bundle_sha256":"a20e3723c45cbc932ec63820da4d53073acff401239caa1e083753cbd20f126b"}}