Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models

Yichen Lyu; Pengkun Yang

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arXiv · 2506.09165

Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models

Yichen Lyu·Pengkun Yang

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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.

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Yichen Lyu, Pengkun Yang. 2025-06-10. Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models. https://arxiv.org/abs/2506.09165

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