>As a side note, I've been doing more probabilistic programming with pymc3 recently, and it's pretty incredible how leaky the abstractions can be. I'm not saying there's a way to do better, just that at present there's a huge gap between the beautiful vision of "the inference button" and the current tools.

Yeah, there's a pretty active debate in the probabilistic programming R&D community over whether it's a bug to sell people on "the inference button", then deliver a leaky abstraction, or a feature to offer richly programmable inference. Our lab has been working on some ideas to get "basic" and "advanced" inference techniques and generative models to compose together nicely to try and build a bridge between the two options[1]

[1] https://drive.google.com/file/d/1bv8g7KTgpgRLsx3ZcaPzIlhGzSa..., https://arxiv.org/abs/1811.05965