pgm.HelloWorld() with Wainwright & Jordan

I have recently came across Wainwright & Jordan's paper on exponential families, graphical models, and variational inference and found it to be quite comprehensive and unifying introduction of the topic. Probabilistic graphical models use a graph-based representation as the basis for compactly encoding a complex distribution over a high-dimensional space. If you are familiar with Koller and Friedman's work on Probabilistic Modeling, Wainwright and Jordan's paper would provide a less mathenamtically terse and more unifying view of the area.

Graphical Models, Exponential Families, and Variational Inference

As compared to Pearl's work on Causality, this paper provides a contemporary look at Message-passing Algorithms for Approximate Inference, Connection to Max-Product Message-Passing and detailed insight into Moment Matrices, Semidefinite Constraints, and Conic Programming Relaxation. Due to it's clarity and detailed explanation, the background material on Graphs, hypergraphs, exponential families and duality is definitely worth reading even if you don't need a refresher.

In Lieu of Pearl's polytree approach, Wainwright & Jordan's work discusses Graphical Models as Exponential Families before delving into Computational Challenges with High-Dimensional Models. Later chapters deal with Sum-Product, Bethe–Kikuchi, and Expectation-Propagation, Mean Field Methods, Variational Methods in Parameter Estimation, Convex Relaxations and Upper Bounds, Integer Programming, Max-product, and Linear Programming Relaxations concluding with Moment Matrices, Semidefinite Constraints, and Conic Programming Relaxation. For a computer scientist, it is always interesting to observe the statistical perspective of machine learning. This contemporary insight into Graphical Models, Exponential Families, and Variational Inference was published in Foundations and Trends in Machine Learning which is definitely built upon researchers' earlier work on Variational inference for Dirichlet process mixtures and Variational inference in graphical models: The view from the marginal polytope.

As an appetizer, I would also recommend Bishop's chapter on Graphical Model.