I realize you infer the model structure and parameters from data. However, in some cases, you might want to find a GM for insight, just as you might want to calculate the mean or median for insight. And just as we can visualize the mean, we have ways of visualizing the graphical model.
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BayesDB does this, essentially. It learns a joint probability distribution over all columns when given tabular data. You can visualize dependencies among columns and cluster rows and much more. Just throw your data in, and explore.
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