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
@article{arxiv.2506.09165,
title = {Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models},
author = {Yichen Lyu and Pengkun Yang},
journal= {arXiv preprint arXiv:2506.09165},
year = {2025}
}