Conditional Expectations on Graphical Models

Actually in most graphical models conditionals are easy and marginals are hard. If your model is not a tree computing the marginals requires some heavy lifting (sampling, variational, junction tree, etc), while the factors in the factor graph give you the conditionals right away. Just take the expression for the full joint likelihood, which is a product of factors over subsets of variables, and fix the values of the variables you know. Drop all the constant terms, and there you have your conditional distribution, which is always a smaller graphical model, so you can use your favorite marginal inference algorithm on this graphical model to compute the expectations (of course, if you only have one or two variables it might be possible to just get the expectations out of the density function, without running any algorithm).

Does this make sense?