Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models

Yichen Lyu, Pengkun Yang
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:3879-3880, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v291-lyu25a, 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}, pages = {3879--3880}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/lyu25a/lyu25a.pdf}, url = {https://proceedings.mlr.press/v291/lyu25a.html}, 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.} }
Endnote
%0 Conference Paper %T Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models %A Yichen Lyu %A Pengkun Yang %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-lyu25a %I PMLR %P 3879--3880 %U https://proceedings.mlr.press/v291/lyu25a.html %V 291 %X 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.
APA
Lyu, Y. & Yang, P.. (2025). Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:3879-3880 Available from https://proceedings.mlr.press/v291/lyu25a.html.

Related Material