What is the relationship between Probabilistic Graphical Models and Graph Neural Networks? I would like to learn more about one or both of these. I incline towards Bayesian networks and PGMs but since Battaglia et al, 2018 I have had half an eye on the various kinds of GNN.
You seem to be able to do similar things with both PGMs and GNNs - inference and learning (of probabilities/weights and of structure) on graphs.  Do the two have different strengths?
Are they just rival academic camps? eg the new book "Deep Learning on Graphs" (Ma & Tang, 2021) doesn't have Koller & Friedman, 2009 in the bibliography & doesn't mention the term "graphical model".
Are the approaches complementary or antagonistic?
References
Battaglia et al., 2018, "Relational inductive biases, deep learning, and graph networks", https://deepmind.com/research/publications/relational-inductive-biases-deep-learning-and-graph-networks
Koller & Friedman, 2009, " Probabilistic Graphical Models: Principles and Techniques", https://mitpress.mit.edu/books/probabilistic-graphical-models
Ma & Tang, 2021, "Deep Learning on Graphs"  http://cse.msu.edu/~mayao4/dlg_book/
 A: So PGMs and GNNs are very different. Don't let the names fool you :). The big application of Probabilistic Graphical Models (PGM), as far as I have seen, has to do with probability queries. One of the most common examples of a PGM is this situation where a person opens their door and finds the pavement wet. What is the probability that it rained outside, versus what is the probability that the sprinklers ran overnight.
In more realistic cases, there might be could be multiple noisy sensor inputs that give information about the state of a system. There could be correlation between the sensor readings, or different states could produce similarities between some sensor readings and differences in others, etc. Hence, by factoring the chain of relationships in the PGM, we can obtain more accurate probabilities for quantities/state of interest, given all of the inputs. The alternative might be some sort of logistic regression, but that would not necessarily incorporate the rich dependencies modelled by a PGM.
On the other hand, GNNs are used for a variety of different applications. There are common applications such as node classification and edge detection. For example, say you are looking at product recommendations and you want to classify whether a recommender is either legitimate or potentially nefarious/unreliable. If you look at the relationships that this recommender has with other known recommenders--and you know whether those known recommenders are reliable/unreliable--then you can classify the original recommender. Alternatively you can predict links between nodes based upon node level covariates and the existing pattern of links in the network.
There are of course may other applications of GNNs, and the two examples I gave are only a flavor of what you can do.
So PGMs and GNNs both incorporate information from the relationships between nodes, as well as node level information itself. But it is quite understandable that a person writing a book on GNNs would not cite the Koller and Friedman book, since the methods and applications are so different between models.
