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Hi, I have a question regarding the design of a directed graphical model. In a toy version of my problem I have some observed variables O1 and O2 and an unobserved variable U. Now, the next step is to define the conditional distributions that govern P(O1,O2,U), so we can write it in the typical Bayes net form. Now, in most cases, I the conditional distributions are set to describe how the unobserved variable generates the data (like a naive bayes). I understand that one reason for this is that if you have a lot of observed variables, this is beneficial because the joint distribution factorizes naturally. However, in my case, it is easy to write P(U|02) but hard to specify P(02|U). So the easiest graph for my model would be: O2--->U--->O1 Conditioned on U O2 and O1 are still independent. Essentially the general "strategy" would be to find the easiest conditional distributions that make sense and draw your graph based on that. Is there anything against such a setup? What steps do you follow when creating a model? Thanks, Roderick |
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Ideally, edges C->E should reflect a cause/effect relationship, i.e., an effect E depends on cause C. This is generally more natural for people to understand and interpret. In your example, I imagine O2->U->O1 represents a system where O1 is an observable output that depends on an unknown U, which in turn depends on a known system input O2. Moreover, you only want edges C->E that reflect direct, not indirect, causes. Extraneous parents means you need to specify/learn more parameters. Thanks arthur, Why do we want it to reflect a cause/effect relationship? Is there a practical reason for it? In my case, O is description of a task as given by a user, and U is a sequence of steps the computer needs to execute in order to complete the task. I find it more simple to describe P(U|O), which would represent the likelihood of having to do sequence U for the given task description, than the opposite P(O|U). In some sense, this could be interpreted as the description causing the sequence. Is it uncommon to have the hidden variable as a child of the observations? If I were to follow this construction of using P(U|01) and P(U|02), all Os would be parents of U and the distribution P(U|O1,O2) would not factorize into P(U|01)*P(U|02) from the graph construction. I could force them to be independent, but somehow I dont see the point in representing my model through a graph.
(Jan 10 '12 at 10:02)
Roderick Nijs
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