I literally spent a whole day arguing with Blake Richards about this on Twitter a few months ago.
Seriously though, approximate backprop seems simpler than approximate PGM inference... and many probabilistic inference problems can be re-framed as neural nets as the field is doing now
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And there are things like:https://www.nature.com/articles/s41467-017-00181-8 …
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And PGMs have been heavily explored, while backprop was ignored for a long time... so I think things are OK
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