{"id":"W3168604437","doi":"10.48550/arxiv.2106.08443","title":"Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nyström Method, and Use of Kernels in Machine Learning: Tutorial and Survey","year":2021,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Neural Networks and Applications","field":"Computer Science","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Reproducing kernel Hilbert space; Representer theorem; Hilbert space; Eigenfunction; Kernel (algebra); Mathematics; Space (punctuation); Kernel method; Applied mathematics; Computer science; Algebra over a field; Calculus (dental); Artificial intelligence; Algorithm; Pure mathematics; Kernel principal component analysis; Eigenvalues and eigenvectors; Support vector machine; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001586356,0.001303474,0.001370707,0.002642103,0.0003573031,0.001356654,0.000695043,0.001350624,0.003360971],"category_scores_gemma":[0.002766806,0.0005226062,0.0008087365,0.00419914,0.001581941,0.004194797,0.0008985145,0.00244023,0.001579554],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007611532,"about_ca_system_score_gemma":0.0008934839,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001105049,"about_ca_topic_score_gemma":0.0006158735,"domain_scores_codex":[0.9993051,0.0002044152,0.00006739861,0.0001388533,0.0002456524,0.00003851774],"domain_scores_gemma":[0.9989594,0.0007146174,0.00007169779,0.00006323363,0.000158056,0.00003294431],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00006637219,0.0001470233,0.001336191,0.003945176,0.0001731465,0.0002665486,0.0004687778,0.01510762,0.002865806,0.4381575,0.04901904,0.4884468],"study_design_scores_gemma":[0.00001677414,0.0001868422,0.002756409,0.0008556892,0.0000933483,0.001598979,0.0002110388,0.04908577,0.002943439,0.5413355,0.4007806,0.0001355949],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"review","genre_gemma":"review","genre_scores_codex":[0.005294905,0.5594575,0.4032256,0.003260238,0.00164797,0.00005668727,0.0003325274,0.0005495354,0.02617498],"genre_scores_gemma":[0.1095804,0.6997364,0.1638791,0.001709068,0.007182183,0.0002155251,0.000931696,0.0004134991,0.01635226],"genre_candidate":"review","genre_consensus":"review","teacher_disagreement_score":0.003360971,"threshold_uncertainty_score":0.01124352,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08495214814039256,"score_gpt":0.2186239364882141,"score_spread":0.1336717883478215,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}