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        "description": "The target is the 2010 estimator, with equal-size independent data/noise samples and known evaluable noise density positive on the data support. Correct model specification, convergence and appropriate identification conditions matter. Unique density recovery does not imply unique parameters: locally full-rank information can coexist with two parameters generating the same Gaussian density. Parameter consistency therefore needs global identifiability or an explicitly separated equivalence-class target; the omitted 2010 proofs are not independently accepted. Only selected 2012 theory pages were checked, and later arbitrary noise-ratio results are not backdated. Noise choice affects information and computing cost, and optimization is not guaranteed globally successful. Synthetic comparisons depend on approximations, initialization, sample selection and method-specific budgets; no universal speed advantage or exact MLE efficiency is asserted. Experiments were not replayed. The contribution is human-authored statistical methodology, not autonomous AI research;.",
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      "statement": "# NCE: learning a statistical model by contrasting data with noise\n\nNoise-contrastive estimation learns an unnormalized statistical model by distinguishing observed data from samples drawn from a known noise distribution, treating the normalization constant as a learnable parameter.\n\nA probability model normally needs a normalizing constant before its likelihood can be evaluated. NCE instead asks whether each observation resembles real data or a known noise source. Its binary-classification objective can learn the statistical parameters and the normalization together. This avoids computing a difficult partition function directly, but works only under suitable support, model and identification conditions. Different parameter labels can still describe the same distribution, so parameter uniqueness must be checked separately.\n\n## Scientific scope\n\nThe target is the 2010 estimator, with equal-size independent data/noise samples and known evaluable noise density positive on the data support. Correct model specification, convergence and appropriate identification conditions matter. Unique density recovery does not imply unique parameters: locally full-rank information can coexist with two parameters generating the same Gaussian density. Parameter consistency therefore needs global identifiability or an explicitly separated equivalence-class target; the omitted 2010 proofs are not independently accepted. Only selected 2012 theory pages were checked, and later arbitrary noise-ratio results are not backdated. Noise choice affects information and computing cost, and optimization is not guaranteed globally successful. Synthetic comparisons depend on approximations, initialization, sample selection and method-specific budgets; no universal speed advantage or exact MLE efficiency is asserted. Experiments were not replayed. The contribution is human-authored statistical methodology, not autonomous AI research;.\n\n## People and systems\n\nMichael Gutmann; Aapo Hyvärinen\n\n\n\n## Original sources\n\n- [Michael Gutmann and Aapo Hyvärinen, Noise-contrastive estimation: A new estimation principle for unnormalized statistical models (AISTATS 2010,297-304), original conference paper](https://proceedings.mlr.press/v9/gutmann10a/gutmann10a.pdf)\n- [Michael U. Gutmann and Aapo Hyvärinen, Noise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics (JMLR 13,307-361,2012), selected theory follow-up](https://jmlr.csail.mit.edu/papers/volume13/gutmann12a/gutmann12a.pdf)\n- [Ryu, Shah and Wornell, A Unified View on Learning Unnormalized Distributions via Noise-Contrastive Estimation (ICML 2025), selected assumption paragraph](https://jongharyu.github.io/assets/pdf/icml2025b.pdf)\n",
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