Probabilistic graphical models

Statistical machine learning and statistical DSP are built on the foundations of probability theory and random variables. Different techniques encode different dependency structure between these variables. This structure leads to specific algorithms for inference and estimation. Many common dependency structures emerge naturally in this way, as a result, there are many common patterns of inference and estimation that suggest general algorithms for this purpose. So, it becomes important to formalize these algorithms; this is the purpose of this chapter. These general algorithms can often lead to substantial computational savings over more brute-force approaches, another benefit that comes from studying the structure of these models in the abstract.