Can’t answer for the whole industry. The two methods have very complementary strengths and weaknesses—so which one you apply will depend on the constraints of the domain (eg: large amounts of training data vs intelligent priors). If you’re lucky, and the situation enables it, you could build out both and ensemble them and hope to get the best of both worlds.

I still think the software stack for probabilistic programming has a ways to go before it becomes as easy to use as a NN using PyTorch, but it should get there in the near future. I’m personally very very excited about the probabilistic programming approach — conceptually it’s a very smooth segue from structured numerical algorithms, and allows you to really exploit problem structure if you have good domain understanding.

For me, it helps organize a lot of well-known algorithms as special cases of a general framework—which is worthwhile in itself. If I can code in the generic framework, and have the compiler generate the appropriate (optimized) special case algorithm (as one hopes), that’s icing on the cake.