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I can't quite get a grasp of how and where these Probabilistic Logical Graphical Models (or PLGM or Statistical Relational Learning Models) score better than ordinary Probabilistic Graphical Models (PGM).

Background:

Most introductions to PLGM state that these models extend PGM (which are supposed to be probabilistic propositional logic models) to include predicate logic (or first-order logic).

I am not an expert on logic, but my understanding is that you can never do with propositional logic all that you can do with predicate logic. But the examples given for PLGM seem like they can all be implemented even through PGM. Hence my question above.

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They are first-order models in the sense that you can use variables (not random variables!) and predicates to declare your model. This is basically the same as template models (such as dynamic Bayesian networks, but more general).

These languages are basically just model description languages, and their semantics are grounded in ordinary propositional PGMs. This means they cannot describe different models, the description is just more concise.

The corollary is that, given such a concise description, you can potentially exploit a lot of symmetry in the model for more efficient inference (called lifted inference then).

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  • $\begingroup$ If I understand correctly, the advantage of PLGMs is that they can potentially use lesser computing resources for the same (description and) inference tasks as PGMs? $\endgroup$ – GuSuku Nov 15 '14 at 21:09
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    $\begingroup$ @crackjack That's the only "hard" advantage I can think of right now. $\endgroup$ – ziggystar Nov 20 '14 at 19:45

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