{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KCH3P3JKWFLLJ6DGONWSAWDQIR","short_pith_number":"pith:KCH3P3JK","schema_version":"1.0","canonical_sha256":"508fb7ed2ab156b4f866736d205870445e6a36589fb0a9d5a0bfec2d9e5ae482","source":{"kind":"arxiv","id":"1904.09668","version":1},"attestation_state":"computed","paper":{"title":"Kriging in Tensor Train data format","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.ME"],"primary_cat":"stat.CO","authors_text":"Alexander Litvinenko, Dishi Liu, Sergey Dolgov","submitted_at":"2019-04-21T22:01:01Z","abstract_excerpt":"Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical optimal design, and others. However, the approximation of a full tensor by its low-rank format can be computationally formidable. In this work, we incorporate the robust Tensor Train (TT) approximation of covariance matrices and the efficient TT-Cross algorithm into the FFT-based Kriging. It is shown that here the computational complexity of Kriging is reduced "},"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":"1904.09668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2019-04-21T22:01:01Z","cross_cats_sorted":["math.NA","stat.ME"],"title_canon_sha256":"a037bf3f68cdbf50e1ac6732d11d13a1b73a6492101661d6aca2331d28f26806","abstract_canon_sha256":"77f2d5e91409ac41df9bf1d42cd5ea922054dd2387dcd2fa96396c87f4437ee3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:03.684345Z","signature_b64":"HFv/i9jhhS1+asSVL/FkbkGwjYGZM4zKn7fVKsH6gBPXBAmU0AAOQDDJZStJMQ5qrUo5Fm4TMIC9XlfY7JYQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"508fb7ed2ab156b4f866736d205870445e6a36589fb0a9d5a0bfec2d9e5ae482","last_reissued_at":"2026-05-17T23:48:03.683938Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:03.683938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kriging in Tensor Train data format","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.ME"],"primary_cat":"stat.CO","authors_text":"Alexander Litvinenko, Dishi Liu, Sergey Dolgov","submitted_at":"2019-04-21T22:01:01Z","abstract_excerpt":"Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical optimal design, and others. However, the approximation of a full tensor by its low-rank format can be computationally formidable. In this work, we incorporate the robust Tensor Train (TT) approximation of covariance matrices and the efficient TT-Cross algorithm into the FFT-based Kriging. It is shown that here the computational complexity of Kriging is reduced "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09668","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":"1904.09668","created_at":"2026-05-17T23:48:03.683998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.09668v1","created_at":"2026-05-17T23:48:03.683998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09668","created_at":"2026-05-17T23:48:03.683998+00:00"},{"alias_kind":"pith_short_12","alias_value":"KCH3P3JKWFLL","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KCH3P3JKWFLLJ6DG","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KCH3P3JK","created_at":"2026-05-18T12:33:21.387695+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/KCH3P3JKWFLLJ6DGONWSAWDQIR","json":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR.json","graph_json":"https://pith.science/api/pith-number/KCH3P3JKWFLLJ6DGONWSAWDQIR/graph.json","events_json":"https://pith.science/api/pith-number/KCH3P3JKWFLLJ6DGONWSAWDQIR/events.json","paper":"https://pith.science/paper/KCH3P3JK"},"agent_actions":{"view_html":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR","download_json":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR.json","view_paper":"https://pith.science/paper/KCH3P3JK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.09668&json=true","fetch_graph":"https://pith.science/api/pith-number/KCH3P3JKWFLLJ6DGONWSAWDQIR/graph.json","fetch_events":"https://pith.science/api/pith-number/KCH3P3JKWFLLJ6DGONWSAWDQIR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR/action/storage_attestation","attest_author":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR/action/author_attestation","sign_citation":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR/action/citation_signature","submit_replication":"https://pith.science/pith/KCH3P3JKWFLLJ6DGONWSAWDQIR/action/replication_record"}},"created_at":"2026-05-17T23:48:03.683998+00:00","updated_at":"2026-05-17T23:48:03.683998+00:00"}