{"id":"W3207872663","doi":"10.1016/j.jfa.2023.110201","title":"Backward and forward Wasserstein projections in stochastic order","year":2023,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Mathematics; Probability measure; Regular polygon; Applied mathematics; Wasserstein metric; Projection (relational algebra); Duality (order theory); Factorization; Pure mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001126999,0.0001312707,0.0005432976,0.003225445,0.00009125693,0.0000533218,0.00009438219,0.00008005916,0.0003330185],"category_scores_gemma":[0.00100338,0.00009804368,0.0004319658,0.01081169,0.00002938493,0.0002053834,0.0000358567,0.0002745569,0.000020532],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007083915,"about_ca_system_score_gemma":0.00008152059,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002625487,"about_ca_topic_score_gemma":0.0002231211,"domain_scores_codex":[0.9983363,0.0000707598,0.0006507176,0.0001663797,0.0005842402,0.0001915683],"domain_scores_gemma":[0.9984186,0.0004993386,0.0003644253,0.0001340584,0.0004848707,0.00009874872],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"observational","study_design_scores_codex":[0.0006527363,0.00158534,0.1946748,0.0001976574,0.03388969,0.0002459759,0.001922082,0.6643242,0.0009419572,0.02022778,0.07250831,0.008829439],"study_design_scores_gemma":[0.004090723,0.0006651122,0.5842391,0.0001344306,0.02238643,0.0002716826,0.01031193,0.2661733,0.00003395528,0.1048676,0.005777143,0.001048618],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8336067,0.0002413171,0.1635546,0.001752637,0.0002509504,0.0001031999,0.000008882005,0.00003045803,0.0004512952],"genre_scores_gemma":[0.9959133,0.00004894776,0.001664755,0.00004180845,0.0001849163,0.000005948199,0.00001128333,0.00001115484,0.002117844],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3981509,"threshold_uncertainty_score":0.5194658,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04565879890116859,"score_gpt":0.2989803354363609,"score_spread":0.2533215365351923,"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."}}