# Soss.jl

Probabilistic programming via source rewriting
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# Soss

Soss is a library for probabilistic programming.

Let's look at an example. First we'll load things:

``````using MeasureTheory
using Soss
``````

MeasureTheory.jl is designed specifically with PPLs like Soss in mind, though you can also use Distributions.jl.

Now for a model. Here's a linear regression:

``````m = @model x begin
α ~ Lebesgue(ℝ)
β ~ Normal()
σ ~ Exponential()
y ~ For(x) do xj
Normal(α + β * xj, σ)
end
return y
end
``````

Next we'll generate some fake data to work with. For `x`-values, let's use

``````x = randn(20)
``````

Now loosely speaking, `Lebesgue(ℝ)` is uniform over the real numbers, so we can't really sample from it. Instead, let's transform the model and make `α` an argument:

``````julia> predα = predictive(m, :α)
@model (x, α) begin
σ ~ Exponential()
β ~ Normal()
y ~ For(x) do xj
Normal(α + β * xj, σ)
end
return y
end
``````

Now we can do

``````julia> y = rand(predα(x=x,α=10.0))
20-element Vector{Float64}:
10.554133456468438
9.378065258831002
12.873667041657287
8.940799408080496
10.737189595204965
9.500536439014208
11.327606120726893
10.899892855024445
10.18488773139243
10.386969795947177
10.382195272387214
8.358407507910297
10.727173015711768
10.452311211064654
11.076232496702387
11.362009520020141
9.539433052406448
10.61851691333643
11.586170856832645
9.197496058151618
``````

Now for inference! Let's use `DynamicHMC`, which we have wrapped in `SampleChainsDynamicHMC`.

``````julia> using SampleChainsDynamicHMC
[ Info: Precompiling SampleChainsDynamicHMC [6d9fd711-e8b2-4778-9c70-c1dfb499d4c4]

julia> post = sample(m(x=x) | (y=y,), dynamichmc())
4000-element MultiChain with 4 chains and schema (σ = Float64, β = Float64, α = Float64)
(σ = 1.0±0.15, β = 0.503±0.26, α = 10.2±0.25)
``````

## How is Soss different from Turing?

First, a fine point: When people say "the Turing PPL" they usually mean what's technically called "DynamicPPL".

• In Soss, models are first class, and can be composed or nested. For example, you can define a model and later nest it inside another model, and inference will handle both together. DynamicPPL can also handle nested models (see this PR) though I'm not aware of a way to combine independently-defined DynamicPPL models for a single inference pass.
• Soss has been updated to use MeasureTheory.jl, though everything from Distributions.jl is still available.
• Soss allows model transformations. This can be used, for example, to easily express predictive distributions or Markov blanket as a new model.
• Most of the focus of Soss is at the syntactic level; inference works in terms of "primitives" that transform the model's abstract syntax tree (AST) to new code. This adds the same benefits as using Julia's macros and generated functions, as opposed to higher-order functions alone.
• Soss can evaluate log-densities symbolically, which can then be used to produce optimized evaluations for much faster inference. This capability is in relatively early stages, and will be made more robust in our ongoing development.
• The Soss team is much smaller than that of DynamicPPL. But I hope that will change (contributors welcome!)

Soss and DynamicPPL are both maturing and becoming more complete, so the above will change over time. It's also worth noting that we (the Turing team and I) hope to move toward a natural way of using these systems together to arrive at the best of both.

## How can I get involved?

• Contribute documentation or tests
• Ask questions on Discourse or Zulip
• File issues for bugs (or other problems) or feature requests
• Use Soss in your applications, teaching, or blogging
• Get involved in other libraries in the Soss ecosystem:

For more details, please see the documentation.

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