This lecture covers probabilistic topic models, focusing on Latent Dirichlet Allocation (LDA). It explains how LDA models topics as distributions over words, with documents being mixtures of these topics. The instructor discusses the drawbacks of Probabilistic Latent Semantic Indexing (PLSI) and introduces LDA as a solution. The lecture delves into the Dirichlet distribution, which is used to model the distribution of distributions in LDA. It also explores the application of LDA in document clustering and its inference methods, such as MCMC and Variational Bayesian inference. Examples from the TREC-AP corpus are provided to illustrate LDA's effectiveness in soft document clustering. The lecture concludes by discussing LDA variants, extensions, and the general idea of topic models in document analysis.