Minor Touches for ScoreGradELBO (#99)

* fix move log density computation of ScoreGradELBO out of the AD path

* update change the `ScoreGradELBO` objective to be VarGrad underneath

* fix remove unnecessary import

* add basic tests for interface tests of variational objectives

* tweak stepsize for inference test of ScoreGradELBO

* add docstrings to elbo objective forward ad paths

* remove `n_montecarlo` option in the inference tests and just fix it

---------

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Hong Ge <[email protected]>

Author: 3 people

src/objectives/elbo/entropy.jl

@@ -37,10 +37,3 @@ function estimate_entropy(
         -logpdf(q, mc_sample)
     end
 end
-
-function estimate_entropy_maybe_stl(
-    entropy_estimator::AbstractEntropyEstimator, samples, q, q_stop
-)
-    q_maybe_stop = maybe_stop_entropy_score(entropy_estimator, q, q_stop)
-    return estimate_entropy(entropy_estimator, samples, q_maybe_stop)
-end

src/objectives/elbo/repgradelbo.jl

@@ -45,6 +45,13 @@ function Base.show(io::IO, obj::RepGradELBO)
     return print(io, ")")
 end
 
+function estimate_entropy_maybe_stl(
+    entropy_estimator::AbstractEntropyEstimator, samples, q, q_stop
+)
+    q_maybe_stop = maybe_stop_entropy_score(entropy_estimator, q, q_stop)
+    return estimate_entropy(entropy_estimator, samples, q_maybe_stop)
+end
+
 function estimate_energy_with_samples(prob, samples)
     return mean(Base.Fix1(LogDensityProblems.logdensity, prob), eachsample(samples))
 end
@@ -85,9 +92,27 @@ function estimate_objective(obj::RepGradELBO, q, prob; n_samples::Int=obj.n_samp
     return estimate_objective(Random.default_rng(), obj, q, prob; n_samples)
 end
 
-function estimate_repgradelbo_ad_forward(params′, aux)
+"""
+    estimate_repgradelbo_ad_forward(params, aux)
+
+AD-guaranteed forward path of the reparameterization gradient objective.
+
+# Arguments
+- `params`: Variational parameters.
+- `aux`: Auxiliary information excluded from the AD path.
+
+# Auxiliary Information 
+`aux` should containt the following entries:
+- `rng`: Random number generator.
+- `obj`: The `RepGradELBO` objective.
+- `problem`: The target `LogDensityProblem`.
+- `adtype`: The `ADType` used for differentiating the forward path.
+- `restructure`: Callable for restructuring the varitional distribution from `params`.
+- `q_stop`: A copy of `restructure(params)` with its gradient "stopped" (excluded from the AD path).
+"""
+function estimate_repgradelbo_ad_forward(params, aux)
     (; rng, obj, problem, adtype, restructure, q_stop) = aux
-    q = restructure_ad_forward(adtype, restructure, params′)
+    q = restructure_ad_forward(adtype, restructure, params)
     samples, entropy = reparam_with_entropy(rng, q, q_stop, obj.n_samples, obj.entropy)
     energy = estimate_energy_with_samples(problem, samples)
     elbo = energy + entropy

src/objectives/elbo/scoregradelbo.jl

@@ -1,113 +1,63 @@
+
 """
 	ScoreGradELBO(n_samples; kwargs...)
 
-Evidence lower-bound objective computed with score function gradients. 
-```math
-\\begin{aligned}
-\\nabla_{\\lambda} \\mathrm{ELBO}\\left(\\lambda\\right)
-&\\=
-\\mathbb{E}_{z \\sim q_{\\lambda}}\\left[
-  \\log \\pi\\left(z\\right) \\nabla_{\\lambda} \\log q_{\\lambda}(z)
-\\right]
-+ \\mathbb{H}\\left(q_{\\lambda}\\right),
-\\end{aligned}
-```
-
-To reduce the variance of the gradient estimator, we use a baseline computed from a running average of the previous ELBO values and subtract it from the objective.
-
-```math
-\\mathbb{E}_{z \\sim q_{\\lambda}}\\left[
-  \\nabla_{\\lambda} \\log q_{\\lambda}(z) \\left(\\pi\\left(z\\right) - \\beta\\right)
-\\right]
-```
+Evidence lower-bound objective computed with score function gradient with the VarGrad objective, also known as the leave-one-out control variate.
 
 # Arguments
-- `n_samples::Int`: Number of Monte Carlo samples used to estimate the ELBO.
-
-# Keyword Arguments
-- `entropy`: The estimator for the entropy term. (Type `<: AbstractEntropyEstimator`; Default: `ClosedFormEntropy()`)
-- `baseline_window_size::Int`: The window size to use to compute the baseline. (Default: `10`)
-- `baseline_history::Vector{Float64}`: The history of the baseline. (Default: `Float64[]`)
+- `n_samples::Int`: Number of Monte Carlo samples used to estimate the VarGrad objective.
 
 # Requirements
 - The variational approximation ``q_{\\lambda}`` implements `rand` and `logpdf`.
 - `logpdf(q, x)` must be differentiable with respect to `q` by the selected AD backend.
 - The target distribution and the variational approximation have the same support.
-
-Depending on the options, additional requirements on ``q_{\\lambda}`` may apply.
 """
-struct ScoreGradELBO{EntropyEst<:AbstractEntropyEstimator} <:
-       AdvancedVI.AbstractVariationalObjective
-    entropy::EntropyEst
+struct ScoreGradELBO <: AbstractVariationalObjective
     n_samples::Int
-    baseline_window_size::Int
-    baseline_history::Vector{Float64}
-end
-
-function ScoreGradELBO(
-    n_samples::Int;
-    entropy::AbstractEntropyEstimator=ClosedFormEntropy(),
-    baseline_window_size::Int=10,
-    baseline_history::Vector{Float64}=Float64[],
-)
-    return ScoreGradELBO(entropy, n_samples, baseline_window_size, baseline_history)
 end
 
 function Base.show(io::IO, obj::ScoreGradELBO)
-    print(io, "ScoreGradELBO(entropy=")
-    print(io, obj.entropy)
-    print(io, ", n_samples=")
+    print(io, "ScoreGradELBO(n_samples=")
     print(io, obj.n_samples)
-    print(io, ", baseline_window_size=")
-    print(io, obj.baseline_window_size)
     return print(io, ")")
 end
 
-function compute_control_variate_baseline(history, window_size)
-    if length(history) == 0
-        return 1.0
-    end
-    min_index = max(1, length(history) - window_size)
-    return mean(history[min_index:end])
-end
-
-function estimate_energy_with_samples(
-    prob, samples_stop, samples_logprob, samples_logprob_stop, baseline
-)
-    fv = Base.Fix1(LogDensityProblems.logdensity, prob).(eachsample(samples_stop))
-    fv_mean = mean(fv)
-    score_grad = mean(@. samples_logprob * (fv - baseline))
-    score_grad_stop = mean(@. samples_logprob_stop * (fv - baseline))
-    return fv_mean + (score_grad - score_grad_stop)
-end
-
 function estimate_objective(
     rng::Random.AbstractRNG, obj::ScoreGradELBO, q, prob; n_samples::Int=obj.n_samples
 )
-    samples, entropy = reparam_with_entropy(rng, q, q, obj.n_samples, obj.entropy)
-    energy = map(Base.Fix1(LogDensityProblems.logdensity, prob), eachsample(samples))
-    return mean(energy) + entropy
+    samples = rand(rng, q, n_samples)
+    ℓπ = map(Base.Fix1(LogDensityProblems.logdensity, prob), eachsample(samples))
+    ℓq = logpdf.(Ref(q), AdvancedVI.eachsample(samples))
+    return mean(ℓπ - ℓq)
 end
 
 function estimate_objective(obj::ScoreGradELBO, q, prob; n_samples::Int=obj.n_samples)
     return estimate_objective(Random.default_rng(), obj, q, prob; n_samples)
 end
 
-function estimate_scoregradelbo_ad_forward(params′, aux)
-    (; rng, obj, problem, adtype, restructure, q_stop) = aux
-    baseline = compute_control_variate_baseline(
-        obj.baseline_history, obj.baseline_window_size
-    )
-    q = restructure_ad_forward(adtype, restructure, params′)
-    samples_stop = rand(rng, q_stop, obj.n_samples)
-    entropy = estimate_entropy_maybe_stl(obj.entropy, samples_stop, q, q_stop)
-    samples_logprob = logpdf.(Ref(q), AdvancedVI.eachsample(samples_stop))
-    samples_logprob_stop = logpdf.(Ref(q_stop), AdvancedVI.eachsample(samples_stop))
-    energy = estimate_energy_with_samples(
-        problem, samples_stop, samples_logprob, samples_logprob_stop, baseline
-    )
-    elbo = energy + entropy
-    return -elbo
+"""
+    estimate_scoregradelbo_ad_forward(params, aux)
+
+AD-guaranteed forward path of the score gradient objective.
+
+# Arguments
+- `params`: Variational parameters.
+- `aux`: Auxiliary information excluded from the AD path.
+
+# Auxiliary Information 
+`aux` should containt the following entries:
+- `samples_stop`: Samples drawn from `q = restructure(params)` but with their gradients stopped (excluded from the AD path).
+- `logprob_stop`: Log-densities of the target `LogDensityProblem` evaluated over `samples_stop`.
+- `adtype`: The `ADType` used for differentiating the forward path.
+- `restructure`: Callable for restructuring the varitional distribution from `params`.
+"""
+function estimate_scoregradelbo_ad_forward(params, aux)
+    (; samples_stop, logprob_stop, adtype, restructure) = aux
+    q = restructure_ad_forward(adtype, restructure, params)
+    ℓπ = logprob_stop
+    ℓq = logpdf.(Ref(q), AdvancedVI.eachsample(samples_stop))
+    f = ℓq - ℓπ
+    return (mean(abs2, f) - mean(f)^2) / 2
 end
 
 function AdvancedVI.estimate_gradient!(
@@ -120,20 +70,15 @@ function AdvancedVI.estimate_gradient!(
     restructure,
     state,
 )
-    q_stop = restructure(params)
-    aux = (
-        rng=rng,
-        adtype=adtype,
-        obj=obj,
-        problem=prob,
-        restructure=restructure,
-        q_stop=q_stop,
-    )
+    q = restructure(params)
+    samples = rand(rng, q, obj.n_samples)
+    ℓπ = map(Base.Fix1(LogDensityProblems.logdensity, prob), eachsample(samples))
+    aux = (adtype=adtype, logprob_stop=ℓπ, samples_stop=samples, restructure=restructure)
     AdvancedVI.value_and_gradient!(
         adtype, estimate_scoregradelbo_ad_forward, params, aux, out
     )
-    nelbo = DiffResults.value(out)
-    stat = (elbo=-nelbo,)
-    push!(obj.baseline_history, -nelbo)
+    ℓq = logpdf.(Ref(q), AdvancedVI.eachsample(samples))
+    elbo = mean(ℓπ - ℓq)
+    stat = (elbo=elbo,)
     return out, nothing, stat
 end

test/inference/repgradelbo_distributionsad.jl

@@ -14,11 +14,10 @@ end
     @testset "$(modelname) $(objname) $(realtype) $(adbackname)" for realtype in
                                                                      [Float64, Float32],
         (modelname, modelconstr) in Dict(:Normal => normal_meanfield),
-        n_montecarlo in [1, 10],
         (objname, objective) in Dict(
-            :RepGradELBOClosedFormEntropy => RepGradELBO(n_montecarlo),
+            :RepGradELBOClosedFormEntropy => RepGradELBO(10),
             :RepGradELBOStickingTheLanding =>
-                RepGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
+                RepGradELBO(10; entropy=StickingTheLandingEntropy()),
         ),
         (adbackname, adtype) in AD_repgradelbo_distributionsad
 

test/inference/repgradelbo_locationscale.jl

@@ -10,16 +10,15 @@ else
     )
 end
 
-@testset "inference ScoreGradELBO VILocationScale" begin
+@testset "inference RepGradELBO VILocationScale" begin
     @testset "$(modelname) $(objname) $(realtype) $(adbackname)" for realtype in
                                                                      [Float64, Float32],
         (modelname, modelconstr) in
         Dict(:Normal => normal_meanfield, :Normal => normal_fullrank),
-        n_montecarlo in [1, 10],
         (objname, objective) in Dict(
-            :RepGradELBOClosedFormEntropy => RepGradELBO(n_montecarlo),
+            :RepGradELBOClosedFormEntropy => RepGradELBO(10),
             :RepGradELBOStickingTheLanding =>
-                RepGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
+                RepGradELBO(10; entropy=StickingTheLandingEntropy()),
         ),
         (adbackname, adtype) in AD_repgradelbo_locationscale
 

test/inference/repgradelbo_locationscale_bijectors.jl

@@ -15,11 +15,10 @@ end
                                                                      [Float64, Float32],
         (modelname, modelconstr) in
         Dict(:NormalLogNormalMeanField => normallognormal_meanfield),
-        n_montecarlo in [1, 10],
         (objname, objective) in Dict(
-            :RepGradELBOClosedFormEntropy => RepGradELBO(n_montecarlo),
+            :RepGradELBOClosedFormEntropy => RepGradELBO(10),
             :RepGradELBOStickingTheLanding =>
-                RepGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
+                RepGradELBO(10; entropy=StickingTheLandingEntropy()),
         ),
         (adbackname, adtype) in AD_repgradelbo_locationscale_bijectors
 

test/inference/scoregradelbo_distributionsad.jl

@@ -14,12 +14,7 @@ end
     @testset "$(modelname) $(objname) $(realtype) $(adbackname)" for realtype in
                                                                      [Float64, Float32],
         (modelname, modelconstr) in Dict(:Normal => normal_meanfield),
-        n_montecarlo in [1, 10],
-        (objname, objective) in Dict(
-            :ScoreGradELBOClosedFormEntropy => ScoreGradELBO(n_montecarlo),
-            :ScoreGradELBOStickingTheLanding =>
-                ScoreGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
-        ),
+        (objname, objective) in Dict(:ScoreGradELBO => ScoreGradELBO(10)),
         (adbackname, adtype) in AD_scoregradelbo_distributionsad
 
         seed = (0x38bef07cf9cc549d)
@@ -29,7 +24,7 @@ end
         (; model, μ_true, L_true, n_dims, strong_convexity, is_meanfield) = modelstats
 
         T = 1000
-        η = 1e-5
+        η = 1e-4
         opt = Optimisers.Descent(realtype(η))
 
         # For small enough η, the error of SGD, Δλ, is bounded as

test/inference/scoregradelbo_locationscale.jl

@@ -15,12 +15,7 @@ end
                                                                      [Float64, Float32],
         (modelname, modelconstr) in
         Dict(:Normal => normal_meanfield, :Normal => normal_fullrank),
-        n_montecarlo in [1, 10],
-        (objname, objective) in Dict(
-            :ScoreGradELBOClosedFormEntropy => ScoreGradELBO(n_montecarlo),
-            :ScoreGradELBOStickingTheLanding =>
-                ScoreGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
-        ),
+        (objname, objective) in Dict(:ScoreGradELBO => ScoreGradELBO(10)),
         (adbackname, adtype) in AD_scoregradelbo_locationscale
 
         seed = (0x38bef07cf9cc549d)
@@ -30,7 +25,7 @@ end
         (; model, μ_true, L_true, n_dims, strong_convexity, is_meanfield) = modelstats
 
         T = 1000
-        η = 1e-5
+        η = 1e-4
         opt = Optimisers.Descent(realtype(η))
 
         # For small enough η, the error of SGD, Δλ, is bounded as

test/inference/scoregradelbo_locationscale_bijectors.jl

@@ -15,12 +15,7 @@ end
                                                                      [Float64, Float32],
         (modelname, modelconstr) in
         Dict(:NormalLogNormalMeanField => normallognormal_meanfield),
-        n_montecarlo in [1, 10],
-        (objname, objective) in Dict(
-            #:ScoreGradELBOClosedFormEntropy => ScoreGradELBO(n_montecarlo), # not supported yet.
-            :ScoreGradELBOStickingTheLanding =>
-                ScoreGradELBO(n_montecarlo; entropy=StickingTheLandingEntropy()),
-        ),
+        (objname, objective) in Dict(:ScoreGradELBO => ScoreGradELBO(10)),
         (adbackname, adtype) in AD_scoregradelbo_locationscale_bijectors
 
         seed = (0x38bef07cf9cc549d)
@@ -30,7 +25,7 @@ end
         (; model, μ_true, L_true, n_dims, strong_convexity, is_meanfield) = modelstats
 
         T = 1000
-        η = 1e-5
+        η = 1e-4
         opt = Optimisers.Descent(realtype(η))
 
         b = Bijectors.bijector(model)