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Title: High-dimensional asymptotics for single-index models via approximate message passing Authors:  Yoshimasa Uematsu - Hitotsubashi University (Japan) [presenting]
Kazuma Sawaya - The University of Tokyo (Japan)
Masaaki Imaizumi - The University of Tokyo (Japan)
Abstract: The purpose is to investigate the precise asymptotic behavior of some estimators for single-index models with unknown links in a high-dimensional setting. Unlike the conventional non-asymptotic scheme, our setting allows a non-sparse coefficient vector while the dimension diverges proportionally with the sample size. Extending the generalized approximate message passing (GAMP) framework, we first uncover the bias in the asymptotic distribution caused by the non-sparse high-dimensionality and then propose a bias-corrected estimator. Finally, numerical experiments confirm the validity of our method.