On the Invertibility of Prediction Models

The function, whose input and output have a one-to-one correspondence, is said to be invertible. This study focuses on the invertibility constraint and reviews recent studies on invertible prediction models. Additionally, as part of our research Okuno and Imaizumi (2024), we discuss how strong the i...

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Bibliographic Details
Published inJournal of the Japan Statistical Society, Japanese Issue Vol. 54; no. 2; pp. 205 - 220
Main Author Okuno, Akifumi
Format Journal Article
LanguageJapanese
Published Japan Statistical Society 04.03.2025
一般社団法人 日本統計学会
Subjects
ノンパラメトリック推定
ミニマックスレート
可逆性
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ISSN0389-5602
2189-1478
DOI10.11329/jjssj.54.205

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Summary:The function, whose input and output have a one-to-one correspondence, is said to be invertible. This study focuses on the invertibility constraint and reviews recent studies on invertible prediction models. Additionally, as part of our research Okuno and Imaizumi (2024), we discuss how strong the invertibility constraint is compared to existing conditions such as the Lipschitz constraint from the perspective of minimax rates. Furthermore, we introduce a nonparametric invertible estimator and demonstrate that it achieves the minimax optimality.
ISSN:0389-5602
2189-1478
DOI:10.11329/jjssj.54.205