Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models
Abstract
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework applicable to diverse statistical settings. Our results rigorously demonstrate how increased dimensionality, coupled with diversity in variables, inherently facilitates identifiability. For the estimation problem, we establish near-optimal minimax rate bounds for the high-dimensional nonparametric density estimation under latent structures with smooth marginals. Contrary to the conventional curse of dimensionality, our sample complexity scales only polynomially with the dimension. Additionally, we develop a perturbation theory for component recovery and propose a recovery procedure based on simultaneous diagonalization.
Cite
Text
Lyu and Yang. "Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models." Proceedings of Thirty Eighth Conference on Learning Theory, 2025.Markdown
[Lyu and Yang. "Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models." Proceedings of Thirty Eighth Conference on Learning Theory, 2025.](https://mlanthology.org/colt/2025/lyu2025colt-identifiability/)BibTeX
@inproceedings{lyu2025colt-identifiability,
title = {{Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models}},
author = {Lyu, Yichen and Yang, Pengkun},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
year = {2025},
pages = {3879-3880},
volume = {291},
url = {https://mlanthology.org/colt/2025/lyu2025colt-identifiability/}
}