This chapter extends foundational knowledge of Probabilistic Graphical Models (PGMs). We focus on advanced techniques for learning, inference, and application within the PGM framework, particularly for Bayesian Networks.

You will examine methods for learning the structure of Bayesian Networks directly from data and contrast them with Bayesian approaches for parameter estimation within a given structure. The discussion then progresses to sophisticated inference algorithms. We will cover the Junction Tree algorithm for exact inference in complex graphs and study how approximate methods, such as MCMC and Variational Inference, are adapted for large or intractable PGMs.

Finally, the chapter provides a detailed look at Latent Dirichlet Allocation (LDA) as a practical application of Bayesian graphical models for topic modeling. You will learn the Bayesian formulation of LDA and implement inference techniques including Collapsed Gibbs Sampling and Variational Bayes to analyze text data. Practical implementation aspects and model evaluation are included.