{"id":"W4416247092","doi":"10.48550/arxiv.2510.19516","title":"Probabilistic PCA on tensors","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Tensor decomposition and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Toronto","keywords":"Identifiability; Multilinear map; Probabilistic logic; Principal component analysis; Estimator; Tensor (intrinsic definition); Kronecker delta; Gaussian; Sparse PCA; Expectation–maximization algorithm","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":[0.004536956,0.001984866,0.001330827,0.002371069,0.00110115,0.002976423,0.001821492,0.001621165,0.00376856],"category_scores_gemma":[0.01947781,0.001184623,0.001684105,0.003010393,0.004362142,0.005448311,0.004481163,0.004212562,0.001572854],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001389191,"about_ca_system_score_gemma":0.001815995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002781588,"about_ca_topic_score_gemma":0.002163239,"domain_scores_codex":[0.9956671,0.001907406,0.0001998955,0.000897633,0.001096319,0.0002316278],"domain_scores_gemma":[0.9907787,0.004511078,0.001070137,0.00196127,0.001372868,0.0003058555],"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":[0.0000519079,0.00002685965,0.000603005,0.0002001618,0.00007748422,0.0000876588,0.0001672226,0.1288474,0.002568681,0.8007486,0.004376158,0.06224494],"study_design_scores_gemma":[0.000006941295,0.000030587,0.0003432693,0.00004498785,0.00001540261,0.00008327422,0.00002513222,0.4391924,0.0009897649,0.5536906,0.005545615,0.00003213218],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.00154927,0.0002442694,0.996841,0.0002082792,0.00003321258,0.00001839498,0.000108995,0.0001263871,0.0008701891],"genre_scores_gemma":[0.2058009,0.003006965,0.7807791,0.0005240595,0.0007002432,0.0003919058,0.001275653,0.0005227696,0.00699852],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.004536956,"threshold_uncertainty_score":0.02399403,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09097254457846796,"score_gpt":0.341070032919232,"score_spread":0.2500974883407641,"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."}}