2 Graphical Models in a Nutshell

2 Graphical Models in a Nutshell Daphne Koller, Nir Friedman, Lise Getoor and Ben Taskar Probabilistic Graphical Models are an elegant framework which combines uncer- tainty (probabilities) and logical structure (independence constraints) to compactly represent complex, real-world phenomena. The framework is quite general in that many of the commonly proposed statistical Models (Kalman lters, hidden Markov Models , Ising Models ) can be described as Graphical Models . Graphical Models have enjoyed a surge of interest in the last two decades, due both to the exibility and power of the representation and to the increased ability to e ectively learn and perform inference in large networks. Introduction Graphical Models [11, 3, 5, 9, 7] have become an extremely popular tool for mod- eling uncertainty.

variablesare assumed to be Boolean.figure 2.1(b) showsthe conditional probability distributions for each of the random variables. We use initials P, T, I, X,andS for shorthand. At the roots, we have the prior probability of the patient having each disease. The probability that the patient does not have the disease a priori

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