How does explaining away cause problems for learning? In one of his lectures Geoff Hinton explains that a big problem of sigmoid belief nets is the explaining away phenomenon. I didn't fully understand this. I see that the induced width of the graph representing Variable Elimination might increase due to the fill-in edges being introduced at the V structures. But is there a more intuition-based way to see this, rather than an appeal to the rigor of the induced graph? 
Consider a simple example where the RVs are: did an earthquake occur, did a burglary occur, and did an alarm trigger. The graph is a V structure with the Earthquake and the Burglary as the parents and the Alarm as the child. If a human being were to try and reason about the true $P(Alarm|Earthquake)$ or $P(Alarm|Burglary)$ what sort of difficulty would this V-structured relationship cause?
 A: The only problem I can see from such a "V structure" is that you have two "causes" - this means that there may be difficulty untangling the effect of each "parent".  In terms of your example, it could be the case that you observe "earthquake" and "burglary" together (both "on" or both "off").  So you would get a good estimate for the value $ P (alarm|earthquake \cup burglary) $ but not the marginal effects.  This is the equivalent of multicolinearity in linear regression.  If you are using the vector $ (e_i, b_i, a_i) $ (e for earthquake, etc) and assuming a binomial model your probability for the ith data point is $ p_i=e_i\theta_e + b_i\theta_b $.  The probabilities in question are $ Pr (alarm|earthquake)=\theta_e + Pr (burglary|earthquake)\theta_b $ and then $ Pr (alarm|burglary)=\theta_b + Pr (earthquake|burglary) \theta_e $
If you only observe them together $ (e_i=1, b_i=1) $ or $(e_i=0, b_i=0) $, then both probabilities are $\theta_b + \theta_e $.  This means that the data is unhelpful in choosing which variable to keep.
