标题： 高维潜变量模型的变分推断 显示英文标题

标题： Variational Inference for Latent Variable Models in High Dimensions

摘要： 变分推理（VI）是贝叶斯推断和概率机器学习中用于近似难以处理的后验分布的一种流行方法。 本文介绍了一种通用框架，用于量化平均场变分推理（MFVI）在具有分类局部潜在变量的贝叶斯潜在变量模型中后验近似的统计准确性。 利用我们的通用框架，我们在著名的潜在狄利克雷分配（LDA）模型中捕获了MFVI“起作用”的精确渐近区域。 专注于混合成员随机块模型（MMSB），我们表明文献中常用的普通完全因子化MFVI是次优的。 我们为此模型提出了一种部分分组VI算法，并证明它有效，并推导出其精确的渐近性能。 我们进一步说明，对于上述两种模型，我们的界是紧的。 显示英文摘要

摘要： Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical accuracy of mean-field variational inference (MFVI) for posterior approximation in Bayesian latent variable models with categorical local latent variables. Utilizing our general framework, we capture the exact asymptotic regime where MFVI `works' for the celebrated latent Dirichlet allocation (LDA) model. Focusing on the mixed membership stochastic blockmodel (MMSB), we show that the vanilla fully factorized MFVI, often used in the literature, is suboptimal. We propose a partially grouped VI algorithm for this model and show that it works, and derive its exact asymptotic performance. We further illustrate that our bounds are tight for both the above models.