标题： 变分伯努利-冯米塞斯定理与增加的参数维度 显示英文标题

标题： Variational Bernstein-von Mises theorem with increasing parameter dimension

摘要： 变分贝叶斯（VB）为高维和大规模推断提供了一种计算高效的替代方法，与马尔可夫链蒙特卡罗相比。然而，现有的VB理论主要集中在固定维设置或特定模型上。为解决这一限制，本文在具有潜在变量的广泛参数模型类中开发了VB的有限样本理论。我们建立了VB后验的理论性质，包括非渐近变分伯恩斯坦-冯·米塞斯定理。此外，我们推导了VB估计量的一致性和渐近正态性。本文以多元高斯混合模型为例进行了说明。 显示英文摘要

摘要： Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings or specific models. To address this limitation, this paper develops a finite-sample theory for VB in a broad class of parametric models with latent variables. We establish theoretical properties of the VB posterior, including a non-asymptotic variational Bernstein--von Mises theorem. Furthermore, we derive consistency and asymptotic normality of the VB estimator. An application to multivariate Gaussian mixture models is presented for illustration.