# Turing support for exact inference (over discrete supports)

**URL:** <https://discourse.julialang.org/t/turing-support-for-exact-inference-over-discrete-supports/70533>\
**Category:** Probabilistic Programming\
**Tags:** question, turing\
**Created:** [October 28, 2021, 4:35am UTC](https://discourse.julialang.org/t/turing-support-for-exact-inference-over-discrete-supports/70533 "2021-10-28T04:35:32Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![jmuchovej](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jmuchovej/32/21640_2.png) [@jmuchovej](https://discourse.julialang.org/u/jmuchovej)\
**Post date:** [October 28, 2021, 4:35am UTC](https://discourse.julialang.org/t/turing-support-for-exact-inference-over-discrete-supports/70533/1 "2021-10-28T04:35:32Z")

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I’m working on a “Rational Speech Acts” (RSA) model. Essentially, RSA is a recursive process where you call distributions over states of the world or utterances made.

So, in this case I have the following setup:

```julia
function literalListener(utterance)
    location ~ locationprior()
    margin ~ marginprior()
    
    # acceptance conditions:
    # if the location is near/inside (within the margin, too) the region
    # don't adjust the logprob, otherwise scale it infinitely 

    # ensure that `location` and `margin` are stacked onto the trace
end

```

then we have something like…

```julia
function pragmaticSpeaker(location, margin)
    utterance ~ utteranceprior()
    L0 ~ listeralListener(utterance)
   
    # acceptance conditions:
    # if the `L0.margin == margin`, accept
    # if `dist(L0.location, location) < epsilon`, accept

    # ensure that `utterance` is stacked onto the trace
end

```

and finally…

```julia
function pragmaticListener(utterance)
    location ~ locationprior()
    margin ~ marginprior()
    
    S1 ~ pragmaticSpeaker(location, margin)

    # acceptance conditions:
    # if S1.utterance == utterance, accept
   
   # ensure taht `location` and `margin` are stacked onto the trace
end

```

Given the `locations`, `margins`, and `utterances` are all finite, (each one has size: 150,000, 3, and 11, respectively) – I believe this is something that could be enumerated, and in fairly reasonable time. (I _think_ the bottlenecks I’m running into with this model in WebPPL stem from an inability to vectorize things like "checking `dist(L0.location, location) < epsilon`. [This is true even if I use less stringent requirements like doing 5K rejection samples, instead of enumerating everything.])

So, this leads me to my questions:

1. **Does Turing.jl support this kind of process?** (I had a stripped down version of RSA working in Gen (it had less than 50 `utterances` + `states`)). But it required bending Gen in ways it doesn’t like. (I have to mix-in “inference machinery” within the modeling because of the acceptance conditions.)
2. **Does Turing.jl support exact enumeration (or similar) over these kinds of [discrete] domains?**

Ideally, I’d be able to extract the posteriors from each of `listeralListener`, `pragmaticSpeaker`, and `pragmaticListener`.

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**Author:** ![dae](https://avatars.discourse-cdn.com/v4/letter/d/47e85d/32.png) [@dae](https://discourse.julialang.org/u/dae)\
**Post date:** [January 31, 2024, 5:05am UTC](https://discourse.julialang.org/t/turing-support-for-exact-inference-over-discrete-supports/70533/2 "2024-01-31T05:05:06Z")

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I was also hoping to find a way to do exact inference over discrete supports in Turing.jl. It looks like it might be possible to implement something like this [Pyro poutine](https://github.com/ebigelow/probmods-pyro/blob/master/pyro_webppl/infer.py#L21) with Turing-contexts.

I just stated playing with Turing.jl a couple days ago so I could be totally wrong.

But, since it’s been a couple years since this was asked, I wanted to bump the thread in case someone came up with a great solution, or had a suggestion about where to start.

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<div class="post-metadata">

**Author:** ![torfjelde](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/torfjelde/32/206542_2.png) [@torfjelde](https://discourse.julialang.org/u/torfjelde)\
**Post date:** [February 8, 2024, 12:29pm UTC](https://discourse.julialang.org/t/turing-support-for-exact-inference-over-discrete-supports/70533/3 "2024-02-08T12:29:16Z")

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EDIT: Whoops! Posted what was supposed to be a reply to another thread here 😬 A sec and I’ll give a response to the actual question here.

EDIT 2:

The issue with Turing.jl is that we don’t have access to the DAG, so _automating_ something like this is unfortunately not doable (at the moment).

So the most straight-forward way to achieve this through manual labour is to define a `Distribution` which takes in your continuous parameters and performs the marginalization in the `logpdf` computation.

Alternatively, you can just perform the enumeration right in the model and use `@addlogprob!` to accumulate the probabilities.