{"paper":{"title":"Fast and accurate conditioning for large-scale and online Gaussian process prediction problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Conditioning on a small number of carefully designed linear combinations of observations recovers machine-precision exact conditional distributions for Gaussian process prediction.","cross_cats":["cs.NA","math.NA","stat.ME"],"primary_cat":"stat.CO","authors_text":"Christopher J. Geoga, Samanyu Arora","submitted_at":"2026-05-04T13:29:09Z","abstract_excerpt":"Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\\mathcal{O}(n^3)$, making it prohibitively expensive for large datasets or large numbers of prediction points. While nearest neighbor-based prediction can work well in certain settings, non-pathological circumstances (for example measurement noise) can severely restrict its efficiency. This work presents a complementary approach where one conditions on carefully designed linear combinations of data, which"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For kernel functions that are smooth away from the origin, conditioning on a small number r of such data contrasts can be machine-precision accurate for the full exact conditional distributions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The kernel functions are smooth away from the origin and that the linear combinations (contrasts) can be carefully designed to achieve the claimed accuracy and efficiency.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Conditioning on a small number of carefully designed linear combinations of data enables machine-precision accurate Gaussian process predictions at low cost for large-scale and online problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Conditioning on a small number of carefully designed linear combinations of observations recovers machine-precision exact conditional distributions for Gaussian process prediction.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"901d94a20d3858daa90828e653ed57039023bbd494fe4e01983144deda87539d"},"source":{"id":"2605.02574","kind":"arxiv","version":2},"verdict":{"id":"3869d112-3db5-4a74-b4a1-f3d411afd67f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T01:43:05.842240Z","strongest_claim":"For kernel functions that are smooth away from the origin, conditioning on a small number r of such data contrasts can be machine-precision accurate for the full exact conditional distributions.","one_line_summary":"Conditioning on a small number of carefully designed linear combinations of data enables machine-precision accurate Gaussian process predictions at low cost for large-scale and online problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The kernel functions are smooth away from the origin and that the linear combinations (contrasts) can be carefully designed to achieve the claimed accuracy and efficiency.","pith_extraction_headline":"Conditioning on a small number of carefully designed linear combinations of observations recovers machine-precision exact conditional distributions for Gaussian process prediction."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02574/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T15:38:43.510910Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T03:01:22.396445Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:14:37.482198Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6ac6c9d575d41ebe7802606e8e8acd107015d8ef070a50a03fa1fcc5a397b687"},"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"}