{"id":"W2007755560","doi":"10.1007/s10208-014-9220-1","title":"Improved Bounds on Sample Size for Implicit Matrix Trace Estimators","year":2014,"lang":"en","type":"article","venue":"Foundations of Computational Mathematics","topic":"Stochastic Gradient Optimization Techniques","field":"Computer Science","cited_by":69,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Ciência sem Fronteiras; Natural Sciences and Engineering Research Council of Canada","keywords":"TRACE (psycholinguistics); Estimator; Upper and lower bounds; Gaussian; Matrix (chemical analysis); Unit vector; Monte Carlo method; Probabilistic logic; Multivariate random variable","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":[0.0003884373,0.0001742041,0.0002589968,0.0001997562,0.0002150898,0.0001520132,0.0006070756,0.00006104635,0.0000197088],"category_scores_gemma":[0.002625191,0.0001768271,0.000114069,0.0003806372,0.00007697225,0.0002589796,0.00007451947,0.00006527811,0.00001122508],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005904264,"about_ca_system_score_gemma":0.0001111353,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005041967,"about_ca_topic_score_gemma":8.71406e-7,"domain_scores_codex":[0.9985908,0.00002645892,0.000570579,0.0002779668,0.0003369539,0.0001972689],"domain_scores_gemma":[0.9921371,0.006449233,0.0003896009,0.0004528547,0.000500246,0.00007093728],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00000378448,0.000180516,0.000007206542,0.00006606083,0.00002024476,2.84431e-8,0.0002639081,0.07546687,0.00007711651,0.9219153,0.0003069151,0.00169203],"study_design_scores_gemma":[0.0002307332,0.0001515185,0.00009603035,0.00002234969,0.000009044073,0.000002989754,0.000008300345,0.5406338,0.0002023156,0.458372,0.0001750407,0.00009593689],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.002398886,0.000003643825,0.9955588,0.0005431486,0.0001676599,0.000596743,0.00004152388,0.000274793,0.000414829],"genre_scores_gemma":[0.2274735,3.756116e-7,0.7722277,0.00007305151,0.00002918593,0.0001029938,0.00002863572,0.00001783797,0.00004669142],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.4651669,"threshold_uncertainty_score":0.7210799,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01812313942802826,"score_gpt":0.3075835547097815,"score_spread":0.2894604152817533,"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."}}