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I have variables A, B, C, D, and E. I am interested in building a classifier for A.

I learned a Bayes net structure from the data using greedy search and BIC as a score. Call this network 1. Using cross validation, I got the mean prediction error for node A in network 1.

I then, thought to create a network structure where all the arcs are incoming into A (B->A, C->A, D->A, E->A). Call this network 2.

I also learned a third network that was constrained by having all the arcs in network 2, but could allow additional arcs between B, C, D, and E. Call this network 3.

It seemed to me that the network 2 and network 3 would be better at predicting A because I was forcing all the info in the data as a direct input into predicting A -- i.e. overfitting. So I expected the mean prediction errors (MPE) for these networks to be less than the first network. But instead they were higher.

Also, when I repeated the cross validation several times, the mean prediction error for network 1 was always the same. But the value varied for networks 2 and 3.

Why would networks 2 and 3 have a higher MPE, and why would MPE for those networks be variable while not variable for network 1?

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    $\begingroup$ Do you mean mean absolute prediction error there, or the actual mean of the (signed) prediction errors? $\endgroup$
    – Glen_b
    Commented Nov 2, 2013 at 0:14

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