Graphical models provide a general formalism for large-scale statistical modeling that fruitfully combines aspects of graph theory and probability
theory. I present a general overview of graphical models, focusing on exponential family parameterizations. The restriction to the exponential family allows powerful tools from convex analysis and convex optimization to be brought to bear, yielding new insights
into the design of computationally efficient inference procedures for graphical models. I also discuss ways to move beyond the finite dimensionality inherent to the exponential family, specifically discussing the Dirichlet process and the hierarchical Dirichlet
process. I also discuss inference procedures for these nonparametric models based on the Chinese restaurant process and stick-breaking
representations of random measures.
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