feat: add mean(::ClosedFormExpectation, ::Logpdf{MVNormal}, ::MVNormal)

src/ClosedFormExpectations.jl

@@ -59,6 +59,8 @@ include("Normal/expectation.jl")
 include("Normal/williams/normal.jl")
 include("Normal/williams/normal_mean_variance.jl")
 include("Normal/williams/ef_parametrization.jl")
+# mv normal
+include("MvNormal/expectation.jl")
 
 # gamma
 include("Gamma/Gamma.jl")

src/MvNormal/expectation.jl

@@ -0,0 +1,7 @@
+import Distributions: Laplace, Normal, Rayleigh, params, cdf, std
+import ExponentialFamily: MultivariateNormalDistributionsFamily
+using SpecialFunctions: erf, loggamma
+
+function mean(::ClosedFormExpectation, p::Logpdf{T1}, q::T2) where {T1 <: MultivariateNormalDistributionsFamily, T2 <: MultivariateNormalDistributionsFamily}
+    -kldivergence(q, p.dist) - entropy(q)
+end

src/expressions/distributions/LogGamma.jl

@@ -19,7 +19,7 @@ end
 LogGamma(α::Real, β::Real; check_args::Bool=true) = LogGamma(promote(α, β)...; check_args=check_args)
 LogGamma(α::Integer, β::Integer; check_args::Bool=true) = LogGamma(float(α), float(β); check_args=check_args)
 
-@distr_support LogGamma 0.0 Inf
+@distr_support LogGamma -Inf Inf
 
 #### Conversions
 Base.convert(::Type{LogGamma{T}}, α::S, β::S) where {T <: Real, S <: Real} = LogGamma(T(α), T(β))

test/MvNormal/mean_test.jl

@@ -0,0 +1,11 @@
+@testitem "mean(::ClosedFormExpectation, p::Logpdf{MultivariateNormalDistributionsFamily}, q::MultivariateNormalDistributionsFamily)" begin
+    include("mvnormal_utils.jl")
+
+    rng = StableRNG(123)
+    for _ in 1:10
+        n = rand(rng, 2:10)
+        μ1, Σ1 = rand(rng, n), generate_random_posdef_matrix(rng, n)
+        μ2, Σ2 = rand(rng, n), generate_random_posdef_matrix(rng, n)
+        central_limit_theorem_test(ClosedFormExpectation(), Logpdf(MvNormal(μ1, Σ1)), MvNormal(μ2, Σ2), 10^6)
+    end
+end

test/MvNormal/mvnormal_utils.jl

@@ -0,0 +1,14 @@
+include("../test_utils.jl")
+
+using Distributions
+using ExponentialFamily
+
+function prepare_samples(::MultivariateNormalDistributionsFamily{T}, samples) where {T}
+    return eachcol(samples)
+end
+
+function generate_random_posdef_matrix(rng, d::Int)
+    A = randn(rng, d, d) 
+    A = A'*A
+    return (A + A')/2
+end

test/distributions/loggamma_tests.jl

@@ -4,4 +4,6 @@
     d = LogGamma(1, 1)
     @test convert(LogGamma{Float64}, d) === d
     @test isa(convert(LogGamma{Float32}, d), LogGamma{Float32})
+    @test minimum(d) == -Inf
+    @test maximum(d) == Inf
 end

test/test_utils.jl

@@ -18,10 +18,15 @@ function concentration_rule(expectation, statistical_mean, N, α,sobolev_const,
     return statistical_mean - ϵ < expectation < statistical_mean + ϵ
 end
 
+function prepare_samples(::Any, samples)
+    return samples
+end
+
 function central_limit_theorem_test(::ClosedFormExpectation, f, q, N = 10^6)
     rng = StableRNG(123)
     samples = rand(rng, q, N)
-    transformed_samples = f.(samples)
+    samples = prepare_samples(q, samples)
+    transformed_samples = map(f, samples)
     expectation = mean(ClosedFormExpectation(), f, q)
     result = sigma_rule(expectation, mean(transformed_samples), std(transformed_samples), N)
     if !result