{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008594435,0.0003177146,0.000336852,0.0001111956,0.000268123,0.0002469443,0.00202302,0.0003144112,0.00000507445],"category_scores_gemma":[0.000119436,0.0002374266,0.000310488,0.0001945393,0.00004914806,0.0001740004,0.001541177,0.0005313625,0.00002807934],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005593444,"about_ca_system_score_gemma":0.0003313813,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007755481,"about_ca_topic_score_gemma":0.000007208404,"domain_scores_codex":[0.9980277,0.0001428038,0.0003894278,0.0007957383,0.0002463046,0.0003980432],"domain_scores_gemma":[0.9976352,0.0003801873,0.0002165545,0.001524387,0.0001651926,0.00007842007],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002948682,0.0001188592,0.0007099193,0.0003170732,0.0002241253,0.000006621416,0.0009281185,0.0008892893,0.0006181232,0.05953256,0.008049943,0.9285759],"study_design_scores_gemma":[0.0005722487,0.00006425646,0.01189805,0.0002293638,0.0001705688,0.000003901691,0.00001219386,0.4268076,0.001999175,0.548681,0.008982532,0.000579106],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.004997233,0.0009779814,0.9841269,0.003559948,0.004065547,0.0009451996,0.00002613627,0.0002131198,0.001087983],"genre_scores_gemma":[0.10505,0.0001476401,0.8910641,0.001825549,0.0005265784,0.0004561249,0.00003137872,0.00002290928,0.0008756947],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.9279968,"threshold_uncertainty_score":0.9681975,"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."}}