Mathematics – Statistics Theory
Scientific paper
2012-01-19
Mathematics
Statistics Theory
26 pages, 5 figures
Scientific paper
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model are estimated conditional on that graph structure. While the probability distributions involved in this second step have been studied in depth, the ones used in the first step have not been explored in as much detail. In this paper, we will study the prior and posterior distributions defined over the space of the graph structures for the purpose of learning the structure of a graphical model. In particular, we will provide a characterisation of their behaviour as a function of the possible edges of the graph and we will derive some properties related to their first and second order moments. We will then illustrate the usefulness of these results in graphical model validation and inference.
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