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Hi,
In most cases, edge factors are values selected by domain experts based on experience, since enough data may not be available to learn the factors. That is, the values in an edge factor are assigned based on correlation between the values of the variables; similarly, a node factor (also called prior) is assigned based on experience.
If there is sufficient data, the factors in an MRF can be learnt from data. However, unfortunately, learning parameters in a MRF is much harder than that in directed models. You can use maximum likelihood estimation but there is no closed form solution. For more details, search for 'parameter learning in Markov random fields'.
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