{"id":"W4415248400","doi":"10.48550/arxiv.2505.03582","title":"Maximum likelihood estimation for the $λ$-exponential family","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Bayesian Methods and Mixture Models","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Exponential family; Maximum likelihood; Dirichlet distribution; Monotone polygon; Regular polygon; Expectation–maximization algorithm; Maximum likelihood sequence estimation; Duality (order theory); Exponential distribution","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006176949,0.0008218584,0.00108386,0.001256703,0.0007584239,0.001686036,0.002359638,0.001686219,0.002421836],"category_scores_gemma":[0.02668852,0.000825324,0.001070176,0.001055494,0.002376582,0.00353071,0.002915986,0.003159647,0.0009536848],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001649586,"about_ca_system_score_gemma":0.001568008,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002656633,"about_ca_topic_score_gemma":0.001860908,"domain_scores_codex":[0.9981295,0.001033984,0.00005896168,0.0003559449,0.0003005954,0.0001210178],"domain_scores_gemma":[0.9927728,0.005622662,0.0003400251,0.00044396,0.0006281269,0.0001925717],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001418123,0.00006026678,0.001181346,0.0001116767,0.00005590503,0.0001111115,0.0001533244,0.3750616,0.002485263,0.5635813,0.002628821,0.05442769],"study_design_scores_gemma":[0.000009556224,0.000009889083,0.0001111618,0.00001157609,0.000003671282,0.00002834398,0.0000105103,0.8816534,0.0005031336,0.1169444,0.0007020279,0.00001236462],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.004765908,0.0001140687,0.9940812,0.0002149704,0.00001343417,0.00001482753,0.00002469449,0.0000800042,0.0006909084],"genre_scores_gemma":[0.2916782,0.0009481355,0.6977943,0.0003192479,0.0001759915,0.0003078937,0.0004936403,0.0003667603,0.007916026],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.006176949,"threshold_uncertainty_score":0.03266722,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04673765752948286,"score_gpt":0.3092937188976755,"score_spread":0.2625560613681927,"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."}}