On the Invertibility of Prediction Models

Abstract

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.