Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula due to their wide range of applications. In this paper, we present a one-week course module for studnets in advanced undergraduate and applied graduate courses on variational inference, a popular optimization-based approach for approximate inference with probabilistic models. Our proposed module is guided by active learning principles: In addition to lecture materials on variational inference, we provide an accompanying class activity, an \texttt{R shiny} app, and guided labs based on real data applications of logistic regression and clustering documents using Latent Dirichlet Allocation with \texttt{R} code. The main goal of our module is to expose students to a method that facilitates statistical modeling and inference with large datasets. Using our proposed module as a foundation, instructors can adopt and adapt it to introduce more realistic case studies and applications in data science, Bayesian statistics, multivariate analysis, and statistical machine learning courses.

翻译：概率模型（如逻辑回归、贝叶斯分类、神经网络及自然语言处理模型）因其广泛的应用场景，在本科与研究生层次的统计学及数据科学课程中日益普及。本文针对高年级本科生与应用型研究生课程，提出一个为期一周的变分推断教学模块。变分推断是一种基于优化的概率模型近似推断方法。本模块以主动学习原则为指导：除变分推断的授课材料外，我们还配套提供课堂互动活动、一个基于R Shiny的应用程序，以及基于逻辑回归和潜狄利克雷分配（Latent Dirichlet Allocation）文档聚类的真实数据R语言引导实验。模块核心目标在于让学生掌握适用于大规模数据统计建模与推断的方法。教师可基于本模块框架进行采纳或调整，在数据科学、贝叶斯统计、多元分析及统计机器学习课程中引入更真实的案例研究与实际应用。