Automatic lazy broadcasting/optimization for arrays of distributions

[ElOceanografo]

This issue follows up on this Discourse discussion. As @mohamed82008 explained, there multiple performance advantages to using a LazyArray inside an arraydist. To realize them, however, one must a) know about this lazy-array trick, and b) remember/look up the LazyArray syntax (which unfortunately includes a macro @~, which is similar but unrelated to Turing/DynamicPPL's ~).

Would it be possible to make the lazy-array trick more automatic? From a user perspective, I can think of a couple of ways this would work:

1. Make arraydist convert its argument to a lazy array automatically (maybe based on some heuristic of when it's likely to benefit performance, and/or an optional argument lazy=true)
2. Provide a macro like @lazyarraydist(...broadcasted computation...) to do the same thing
3. Just make .~ parse to a lazily broadcasted array distribution

If 3) could work, that would be best, though I don't know if it would come with hidden downsides or implementation challenges. Basically, anything that decreases the number of special-case optimization hacks a user has to remember would be great!

[devmotion]

Just a heads up, my plan is to remove arraydist and integrate and generalize it into the product distribution in Distributions.

[ElOceanografo]

Cool, good to know. So would that that resolve the tracked-array vs. array-of-tracked issue @mohamed82008 was referring to in the discourse thread?

[dlakelan]

Hi, following this issue because I'm very interested in what ultimately is going to be the fast way to handle something like this. Currently the most reliable (doesn't cause crashes/backtraces) is for me to do Turing.@addlogprob!(sum(logpdf(....))) all manually.

[yebai]

We will likely adopt #1723 (comment).

In addition, it is better to keep the module macro transparent so more performance optimisation can be done outside DynamicPPL / Turing. #1900 should make this type of performance optimisation easier because the internal SimpleVarInfo data structure becomes more compatible with the Julia ecosystem.