Making use of Symbolics.jl/SymbolicUtils.jl by torfjelde · Pull Request #234 · TuringLang/DynamicPPL.jl

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EDIT: This doesn't work right now as it seems the original rewriters are now out of date.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

 )
    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.

torfjelde · 2021-07-29T22:51:54Z

+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

+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

+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

785242e

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

daa1319

github-actions Bot reviewed Jul 24, 2021

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torfjelde added 2 commits July 24, 2021 16:31

updated symbolize

70c9997

formatting

23141be

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

18ae91b

make it runnable on newer package versions

b19700e

github-actions Bot reviewed Jul 29, 2021

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Comment thread src/symbolic/contexts.jl

torfjelde commented Jul 29, 2021

View reviewed changes

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

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

Dependencies

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