Is there any way to preserve any part of an unsupervised-learned network (especially if you manually added/removed arcs based on prior knowledge) when carrying out any of the supervised learning algorithms? It seems like a waste if I spent time modeling a good representation of the data structure only to have it vanish when performing some target variable analysis.
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Unfortunately, all the BayesiaLab's Supervised Learning algorithms start with a fully unconnected network. There is thus no way to keep any fixed arcs. The only solution would consist in using unsupervised learning (e.g. Taboo with "Keep Structure") in lieu of supervised learning. You can then perform your target variable analysis.
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You can add whatever knowledge you extracted from unsupervised learning to your data file and then use that modified input file with supervised learning algos.  For instance you could add some clusters/factors or manual nodes to your dataset.

Also please take a look at this very useful explanation showing the use of fixed arcs and virtual datasets to express prior knowledge:
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