Tutorial: The difficulty of estimating reversible functions - with generative models in mind
##article.authors##
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Akifumi Okuno
Institute of Statistical Mathematics, School of Statistical Thinking
https://researchmap.jp/aokuno
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Masaaki Imaizumi
Graduate School of Arts and Science, The University of Tokyo
https://researchmap.jp/mimaizumi
DOI:
https://doi.org/10.51094/jxiv.616Keywords:
Invertible function estimation, One-to-one correspondence, Generative model, Strength of constraint, Estimation difficultyAbstract
本稿は Electoronic Journal of Statistics に採択された我々の原著論文: Okuno and Imaizumi (2024) に関する解説です．解説の平易さを優先するため，より厳密な記述については原著論文をご参照ください．
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References
Daneri, S. and Pratelli, A. (2014). Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Annales de l’I.H.P. Analyse non lin´eaire, 31(3):567–589
Ishikawa, I., Teshima, T., Tojo, K., Oono, K., Ikeda, M., and Sugiyama, M. (2023). Universal approximation property of invertible neural networks. Journal of Machine Learning Research, 24(287):1–68
Okuno, A. and Imaizumi, M. (2024). Minimax analysis for inverse risk in nonparametric planer invertible regression. Electronic Journal of Statistics, 18(1):355–394
Teshima, T., Ishikawa, I., Tojo, K., Oono, K., Ikeda, M., and Sugiyama, M. (2020). Coupling-based invertible neural networks are universal diffeomorphism approximators. In Advances in Neural Information Processing Systems, volume 33, pages 3362–3373. Curran Associates, Inc
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Submitted: 2024-02-03 05:54:18 UTC
Published: 2024-02-07 08:45:58 UTC
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Copyright (c) 2024
Akifumi Okuno
Masaaki Imaizumi
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
