Making use of Symbolics.jl/SymbolicUtils.jl #234

torfjelde · 2021-04-27T03:23:57Z

I'm just going to put this here before heading to bed, but there's some more stuff to do here:

Allow making observations/model arguments symbolic. I've verified that this works, but I just haven't gotten around to automatically constructing Variable for the model arguments yet.
Docstrings/tests
???

Anyways, it's pretty dope.

Expression generation
Dependencies

julia> using DynamicPPL, Distributions

julia> @model function demo(x, ::Type{TV} = Vector{Float64}) where {TV}
           # Just to demonstrate that we're not restricted to `x ~ DistKnowAtExpansionTime`
           s_prior = InverseGamma()
           s ~ s_prior

           num_obs = length(x)
           m = TV(undef, num_obs)
           m[1] ~ Normal(0, √s)
           x[1] ~ Normal(x[1], √s)
           for i = 2:num_obs
               m[i] ~ Normal(m[i - 1], √s)
               x[i] ~ Normal(m[i], √s)
           end
           return m, x
       end;

julia> m = demo(randn(10) .+ 1);

Expression generation

EDIT: This doesn't work right now as it seems the original rewriters are now out of date. We can still extract an expression using vi, θ Symbolic.symbolize(m); getlogp(vi) but we won't have tracing through the logpdf computation.

julia> lp, θ = Symbolic.symbolic_logp(m) # can drop the constant in front too if we want
(-18.378770664093455 - (2.0log(θ₁)) - (20log(sqrt(θ₁))) - (0.5abs2(θ₂*(sqrt(θ₁)^-1))) - (0.5abs2((θ₁₀ - θ₉)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₁₁ - θ₁₀)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₃ - θ₂)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₄ - θ₃)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₅ - θ₄)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₆ - θ₅)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₇ - θ₆)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₈ - θ₇)*(sqrt(θ₁)^-1))) - (0.5abs2((θ₉ - θ₈)*(sqrt(θ₁)^-1))) - (0.5abs2((sqrt(θ₁)^-1)*(-1.4166318988896798 - θ₁₀))) - (0.5abs2((sqrt(θ₁)^-1)*(1.9786928906469687 - θ₁₁))) - (0.5abs2((sqrt(θ₁)^-1)*(-0.7713281377661316 - θ₃))) - (0.5abs2((sqrt(θ₁)^-1)*(0.5953344430416955 - θ₄))) - (0.5abs2((sqrt(θ₁)^-1)*(0.4888163369370143 - θ₅))) - (0.5abs2((sqrt(θ₁)^-1)*(0.9869369683122523 - θ₆))) - (0.5abs2((sqrt(θ₁)^-1)*(0.18968854568519278 - θ₇))) - (0.5abs2((sqrt(θ₁)^-1)*(2.20765228354745 - θ₈))) - (0.5abs2((sqrt(θ₁)^-1)*(1.1746311120999957 - θ₉))) - (θ₁^-1), Symbolics.Num[θ₁, θ₂, θ₃, θ₄, θ₅, θ₆, θ₇, θ₈, θ₉, θ₁₀, θ₁₁])

julia> ∂lp = Symbolics.gradient(lp, θ)
11-element Vector{Symbolics.Num}:
                                     θ₁^-2 + 0.5(θ₂^2)*(sqrt(θ₁)^-4) + 0.5(sqrt(θ₁)^-4)*((θ₁₀ - θ₉)^2) + 0.5(sqrt(θ₁)^-4)*((θ₁₁ - θ₁₀)^2) + 0.5(sqrt(θ₁)^-4)*((θ₃ - θ₂)^2) + 0.5(sqrt(θ₁)^-4)*((θ₄ - θ₃)^2) + 0.5(sqrt(θ₁)^-4)*((θ₅ - θ₄)^2) + 0.5(sqrt(θ₁)^-4)*((θ₆ - θ₅)^2) + 0.5(sqrt(θ₁)^-4)*((θ₇ - θ₆)^2) + 0.5(sqrt(θ₁)^-4)*((θ₈ - θ₇)^2) + 0.5(sqrt(θ₁)^-4)*((θ₉ - θ₈)^2) + 0.5(sqrt(θ₁)^-4)*((-1.4166318988896798 - θ₁₀)^2) + 0.5(sqrt(θ₁)^-4)*((1.9786928906469687 - θ₁₁)^2) + 0.5(sqrt(θ₁)^-4)*((-0.7713281377661316 - θ₃)^2) + 0.5(sqrt(θ₁)^-4)*((0.5953344430416955 - θ₄)^2) + 0.5(sqrt(θ₁)^-4)*((0.4888163369370143 - θ₅)^2) + 0.5(sqrt(θ₁)^-4)*((0.9869369683122523 - θ₆)^2) + 0.5(sqrt(θ₁)^-4)*((0.18968854568519278 - θ₇)^2) + 0.5(sqrt(θ₁)^-4)*((2.20765228354745 - θ₈)^2) + 0.5(sqrt(θ₁)^-4)*((1.1746311120999957 - θ₉)^2) - (2.0(θ₁^-1)) - ((10//1)*(sqrt(θ₁)^-2))
  (θ₃ - θ₂)*(sqrt(θ₁)^-2) - (θ₂*(sqrt(θ₁)^-2))
   (θ₄ - θ₃)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(-0.7713281377661316 - θ₃) - ((θ₃ - θ₂)*(sqrt(θ₁)^-2))
    (θ₅ - θ₄)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(0.5953344430416955 - θ₄) - ((θ₄ - θ₃)*(sqrt(θ₁)^-2))
    (θ₆ - θ₅)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(0.4888163369370143 - θ₅) - ((θ₅ - θ₄)*(sqrt(θ₁)^-2))
    (θ₇ - θ₆)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(0.9869369683122523 - θ₆) - ((θ₆ - θ₅)*(sqrt(θ₁)^-2))
    (θ₈ - θ₇)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(0.18968854568519278 - θ₇) - ((θ₇ - θ₆)*(sqrt(θ₁)^-2))
    (θ₉ - θ₈)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(2.20765228354745 - θ₈) - ((θ₈ - θ₇)*(sqrt(θ₁)^-2))
   (θ₁₀ - θ₉)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(1.1746311120999957 - θ₉) - ((θ₉ - θ₈)*(sqrt(θ₁)^-2))
 (θ₁₁ - θ₁₀)*(sqrt(θ₁)^-2) + (sqrt(θ₁)^-2)*(-1.4166318988896798 - θ₁₀) - ((θ₁₀ - θ₉)*(sqrt(θ₁)^-2))
                              (sqrt(θ₁)^-2)*(1.9786928906469687 - θ₁₁) - ((θ₁₁ - θ₁₀)*(sqrt(θ₁)^-2))

julia> ∂f, ∂f! = Symbolics.build_function(∂lp, θ, expression = false);

julia> ∂f(rand(Symbolics.value(length(θ))))
11-element Vector{Float64}:
 26.085486889785475
 -1.1940138187926816
 -0.709786284651692
 -1.8974997722462343
  3.2298551373276108
  0.07043163767794725
  3.301109716439576
  3.527331147067538
  0.6372253272009718
 -7.676985933953628
  3.717132883407671

Dependencies

julia> Symbolic.dependencies(m) # `VarName` -> `VarName`
Dict{VarName, Vector{T} where T} with 11 entries:
  m[5]  => VarName[m[4], s]
  m[4]  => VarName[m[3], s]
  m[8]  => VarName[m[7], s]
  s     => Union{typeof(var), VarName}[]
  m[6]  => VarName[m[5], s]
  m[3]  => VarName[m[2], s]
  m[1]  => [s]
  m[7]  => VarName[m[6], s]
  m[2]  => VarName[m[1], s]
  m[10] => VarName[m[9], s]
  m[9]  => VarName[m[8], s]

julia> Symbolic.dependencies(m, true) # `Symbol` -> `Symbol`
Dict{Symbolics.Num, Vector{T} where T} with 11 entries:
  θ₉  => SymbolicUtils.Sym{Real, Nothing}[θ₈, θ₁]
  θ₇  => SymbolicUtils.Sym{Real, Nothing}[θ₆, θ₁]
  θ₅  => SymbolicUtils.Sym{Real, Nothing}[θ₄, θ₁]
  θ₆  => SymbolicUtils.Sym{Real, Nothing}[θ₅, θ₁]
  θ₃  => SymbolicUtils.Sym{Real, Nothing}[θ₂, θ₁]
  θ₁₀ => SymbolicUtils.Sym{Real, Nothing}[θ₉, θ₁]
  θ₂  => SymbolicUtils.Sym{Real, Nothing}[θ₁]
  θ₁₁ => SymbolicUtils.Sym{Real, Nothing}[θ₁₀, θ₁]
  θ₁  => Any[]
  θ₄  => SymbolicUtils.Sym{Real, Nothing}[θ₃, θ₁]
  θ₈  => SymbolicUtils.Sym{Real, Nothing}[θ₇, θ₁]

Can of course use LightGraphs.jl, etc. to generate visualizations of the models too:

julia> using LightGraphs, MetaGraphs

julia> function graph(m::Model)
           deps = Symbolic.dependencies(m)

           g = MetaDiGraph(length(deps))
           for (i, vn) in enumerate(keys(deps))
               set_prop!(g, i, :vn, vn)
           end
           set_indexing_prop!(g, :vn)

           for vn in keys(deps)
               for parent in deps[vn]
                   add_edge!(g, (g[parent, :vn], g[vn, :vn]))
               end
           end
           return g
       end
graph (generic function with 1 method)

julia> g = graph(m)
{11, 19} directed Int64 metagraph with Float64 weights defined by :weight (default weight 1.0)

julia> using GraphRecipes, Plots

julia> nodelabels = map(vertices(g)) do v
           get_prop(g, v, :vn)
       end;

julia> graphplot(g, names=nodelabels)

Resulting in:

torfjelde · 2021-04-27T03:24:47Z

src/context_implementations.jl

 )
    increment_num_produce!(vi)
-    return Distributions.loglikelihood(dist, value)
+    return sum(Distributions.logpdf(dist, value))


This is left-over from some earlier experimentation I did. We should make loglikelihood a primitive, and then work from there I think.

src/symbolic/Symbolic.jl

src/symbolic/rules.jl

src/varinfo.jl

src/symbolic/contexts.jl

torfjelde · 2021-07-29T22:51:54Z

src/symbolic/Symbolic.jl

+function symbolize(
+    rng::Random.AbstractRNG,
+    m::Model,
+    vi::VarInfo=VarInfo(m);
+    spl=SampleFromPrior(),
+    ctx=DefaultContext(),
+    include_data=false,
+)
+    m(rng, vi, spl, ctx)
+    θ_orig = vi[spl]
+
+    # Symbolic `logpdf` for fixed observations.
+    # TODO: don't `collect` once symbolic arrays are mature enough.
+    Symbolics.@variables θ[1:length(θ_orig)]
+    vi = VarInfo{Real}(vi, spl, θ)
+    m(vi, ctx)
+
+    return vi, θ
+end


Execute model once to get shape of latent variables.

Construct symbolic variables.

Execute model on symbolic variables.

vi (the trace struct) now contains a symbolic representation of the logjoint retrievable through getlogp(vi).

torfjelde · 2021-07-29T22:53:40Z

src/symbolic/Symbolic.jl

+function dependencies(m::Model, symbolic=false)
+    ctx = SymbolicContext(DefaultContext())
+    vi = symbolize(m, VarInfo(m); ctx=ctx)
+
+    return dependencies(ctx, symbolic)
+end


Uses "contextual" dispatch to overload the corresponding *tilde_ statements, stroing the mapping from symbolic variable θ[i] to VarName.

torfjelde · 2021-07-29T22:56:14Z

src/symbolic/rules.jl

+function getlogpdf(d, args)
+    replacements = Dict(:Normal => StatsFuns.normlogpdf, :Gamma => StatsFuns.gammalogpdf)
+
+    dsym = Symbol(d)
+    if haskey(replacements, dsym)
+        return replacements[dsym]
+    else
+        return d
+    end
+end


The idea behind all this was to replace the "non-tracable" logpdf impls from Distributions.jl with traceable impls from StatsFuns.jl. After #292 we could probably avoid this by simply using MeasureTheory.jl instead:)

Also, this is super messy and probably not the greatest; I blame it on the fact that I had no idea what I was doing:)

yebai · 2022-03-17T17:58:56Z

Closed in favour of TuringLang/AbstractPPL.jl#47

relax constraints to allow use with Symbolics.jl

783d81d

torfjelde commented Apr 27, 2021

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torfjelde added 4 commits April 27, 2021 05:25

added symbolic stuff

0421aed

added Symbolic as dependency

14ad023

added version bound to Symbolics

03067a0

added another method for disambiguiation

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torfjelde mentioned this pull request Jul 9, 2021

Better handling of interaction between contexts #274

Closed

torfjelde added 4 commits July 24, 2021 15:23

update Project.toml

a3a9742

Merge branch 'master' into tor/symbolics

284d85d

updated symbolics versioning

817533c

added some hacks to make it at least run

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github-actions bot reviewed Jul 24, 2021

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torfjelde added 2 commits July 24, 2021 16:31

updated symbolize

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formatting

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torfjelde marked this pull request as draft July 24, 2021 15:36

torfjelde force-pushed the tor/symbolics branch from a787e56 to 23141be Compare July 29, 2021 22:35

torfjelde added 2 commits July 29, 2021 23:36

Merge branch 'master' into tor/symbolics

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make it runnable on newer package versions

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torfjelde commented Jul 29, 2021

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yebai closed this Mar 17, 2022

yebai deleted the tor/symbolics branch March 17, 2022 17:59

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Making use of Symbolics.jl/SymbolicUtils.jl #234

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