标题： 高维非参数潜在结构模型中的可识别性与估计 显示英文标题

标题： Identifiability and Estimation in High-Dimensional Nonparametric Latent Structure Models

摘要： 本文研究了高维非参数潜在结构模型中的可辨识性和估计问题。 我们引入了一个广义现有条件的可辨识性定理，建立了一个适用于多种统计设置的统一框架。 我们的结果严格证明了维度增加以及变量多样性如何内在地促进可辨识性。 对于估计问题，我们在具有光滑边缘分布的潜在结构下的高维非参数密度估计中建立了接近最优的 minimax 率界。 与传统的维度灾难相反，我们的样本复杂度仅以多项式形式依赖于维度。 此外，我们发展了成分恢复的摄动理论，并提出了一种基于同时对角化的恢复程序。 显示英文摘要

摘要： 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.