{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LINOKKFXRA2TKCFI2OSCSZUBB4","short_pith_number":"pith:LINOKKFX","schema_version":"1.0","canonical_sha256":"5a1ae528b788353508a8d3a42966810f2bcdf0a29396c455577dec7de764ba0d","source":{"kind":"arxiv","id":"1807.02582","version":1},"attestation_state":"computed","paper":{"title":"Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Bharath K Sriperumbudur, Dino Sejdinovic, Motonobu Kanagawa, Philipp Hennig","submitted_at":"2018-07-06T22:44:10Z","abstract_excerpt":"This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two esse"},"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":"1807.02582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-07-06T22:44:10Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d7027f6d96283b932615826196a7ec9e47a96a09f60edfb0256df6489813d73","abstract_canon_sha256":"0865ecc22c47309c82690a657943e7fd9aaf77a68c9e3ecb627febd868ef33ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:16.657135Z","signature_b64":"hSy3KW+T/MjuG7jQjzFJ3PK/B+DmhIyEQ+GUtg1PjivmVpvaDYLshJz6b9qmieLIAE9RSeItDxKmirLplcXnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a1ae528b788353508a8d3a42966810f2bcdf0a29396c455577dec7de764ba0d","last_reissued_at":"2026-05-18T00:11:16.656339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:16.656339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Bharath K Sriperumbudur, Dino Sejdinovic, Motonobu Kanagawa, Philipp Hennig","submitted_at":"2018-07-06T22:44:10Z","abstract_excerpt":"This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two esse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02582","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":"1807.02582","created_at":"2026-05-18T00:11:16.656469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.02582v1","created_at":"2026-05-18T00:11:16.656469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02582","created_at":"2026-05-18T00:11:16.656469+00:00"},{"alias_kind":"pith_short_12","alias_value":"LINOKKFXRA2T","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LINOKKFXRA2TKCFI","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LINOKKFX","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":13,"internal_anchor_count":8,"sample":[{"citing_arxiv_id":"1906.11655","citing_title":"Uncertainty Estimates for Ordinal Embeddings","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"1910.03120","citing_title":"Gaussian Process Assisted Active Learning of Physical Laws","ref_index":21,"is_internal_anchor":true},{"citing_arxiv_id":"2312.01386","citing_title":"On the Suboptimality of GP-UCB under Polynomial Effective Optimism","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2603.01084","citing_title":"Kernel-Based LMI Approaches to Solving the Hamilton-Jacobi-Bellman Equation and Nonlinear Optimal Control","ref_index":25,"is_internal_anchor":true},{"citing_arxiv_id":"2602.15006","citing_title":"Distributed Quantum Gaussian Processes for Multi-Agent Systems","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14222","citing_title":"Robust and Data-Adaptive Integration of Nonconcurrent Data in Platform Trials via Gaussian Processes","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14142","citing_title":"To discretize continually: Mean shift interacting particle systems for Bayesian inference","ref_index":52,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13160","citing_title":"Kernel-based guarantees for nonlinear parametric models in Bayesian optimization","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2605.11293","citing_title":"Pressure reconstruction from error-embedded gradient measurements: a Gaussian-process generalization of Green's function integration","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10299","citing_title":"Nearly-Optimal Algorithm for Adversarial Kernelized Bandits","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10572","citing_title":"Online Sharp-Calibrated Bayesian Optimization","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25965","citing_title":"Adversarial Robustness of NTK Neural Networks","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20414","citing_title":"Fast and Provably Accurate Sequential Designs using Hilbert Space Gaussian Processes","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4","json":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4.json","graph_json":"https://pith.science/api/pith-number/LINOKKFXRA2TKCFI2OSCSZUBB4/graph.json","events_json":"https://pith.science/api/pith-number/LINOKKFXRA2TKCFI2OSCSZUBB4/events.json","paper":"https://pith.science/paper/LINOKKFX"},"agent_actions":{"view_html":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4","download_json":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4.json","view_paper":"https://pith.science/paper/LINOKKFX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.02582&json=true","fetch_graph":"https://pith.science/api/pith-number/LINOKKFXRA2TKCFI2OSCSZUBB4/graph.json","fetch_events":"https://pith.science/api/pith-number/LINOKKFXRA2TKCFI2OSCSZUBB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4/action/storage_attestation","attest_author":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4/action/author_attestation","sign_citation":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4/action/citation_signature","submit_replication":"https://pith.science/pith/LINOKKFXRA2TKCFI2OSCSZUBB4/action/replication_record"}},"created_at":"2026-05-18T00:11:16.656469+00:00","updated_at":"2026-05-18T00:11:16.656469+00:00"}