{"paper":{"title":"Safe Bayesian Optimization for Uncertain Correlations Matrices in Linear Models of Co-Regionalization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Uniform error bounds extend safety guarantees for multi-task Bayesian optimization to linear models of co-regionalization with uncertain correlations.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.LG","authors_text":"Annika Eichler, Jannis L\\\"ubsen","submitted_at":"2026-05-13T10:14:43Z","abstract_excerpt":"This paper extends safety guarantees for multi-task Bayesian optimization with uncertain correlation matrices from intrinsic co-reginalization models to linear models of co-reginalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-reginalization kernel. Furthermore, we show the potential improvement of performance using linear models of co-reginalization in a numerical comparison on a safe multi-task Bayesian opti"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-reginalization kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the safety guarantees previously derived for intrinsic co-regionalization models transfer directly to linear models of co-regionalization without requiring additional restrictions on the feature composition or the uncertainty in the correlation matrices.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends uniform error bounds and safety guarantees to linear models of co-regionalization kernels for safe multi-task Bayesian optimization, showing performance gains on a benchmark.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Uniform error bounds extend safety guarantees for multi-task Bayesian optimization to linear models of co-regionalization with uncertain correlations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15a15a97f42167ac9838f65eedbc55d290d8d6332779585ee1d7060bb4eb6011"},"source":{"id":"2605.13302","kind":"arxiv","version":1},"verdict":{"id":"f2c47e22-52c5-4c2e-843a-871149144e4c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:23:02.562286Z","strongest_claim":"We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-reginalization kernel.","one_line_summary":"Extends uniform error bounds and safety guarantees to linear models of co-regionalization kernels for safe multi-task Bayesian optimization, showing performance gains on a benchmark.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the safety guarantees previously derived for intrinsic co-regionalization models transfer directly to linear models of co-regionalization without requiring additional restrictions on the feature composition or the uncertainty in the correlation matrices.","pith_extraction_headline":"Uniform error bounds extend safety guarantees for multi-task Bayesian optimization to linear models of co-regionalization with uncertain correlations."},"references":{"count":65,"sample":[{"doi":"","year":2015,"title":"Safe Exploration for Optimization with","work_id":"9c156ee1-f93e-437b-90ec-089cda671a4f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"2006 , number =","work_id":"411e11f1-cb54-4fc5-8bb6-64aa02e3fc00","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Horn, Roger A. , publisher =. 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