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[deps] | ||
ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" | ||
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" | ||
FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b" | ||
FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000" | ||
PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150" | ||
QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" | ||
StatsAPI = "82ae8749-77ed-4fe6-ae5f-f523153014b0" | ||
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" | ||
StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c" | ||
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[compat] | ||
ChainRulesCore = "=1.24.0" | ||
Distributions = "=0.25.111" | ||
FillArrays = "=1.13.0" | ||
FiniteDifferences = "0.12.32" | ||
PDMats = "=0.11.31" | ||
QuadGK = "=2.11.0" | ||
StatsAPI = "=1.7.0" | ||
StatsBase = "=0.34.3" | ||
StatsFuns = "=1.3.1" |
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module DistributionsIntegrationTests | ||
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using Distributions | ||
using Enzyme: Enzyme | ||
using FillArrays: Fill | ||
using FiniteDifferences: FiniteDifferences | ||
using LinearAlgebra: Diagonal, Hermitian, I, Symmetric, diag, cholesky | ||
using PDMats: PDMat | ||
using Random: randn | ||
using Test: @test, @testset | ||
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# TODO(mhauru) Could we at some point make do without this? | ||
Enzyme.API.runtimeActivity!(true) | ||
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""" | ||
Test Enzyme.gradient, both Forward and Reverse mode, against FiniteDifferences.grad, for a | ||
given function f and argument x. | ||
""" | ||
function test_grad(f, x; rtol=1e-6, atol=1e-6) | ||
@nospecialize | ||
finitediff = FiniteDifferences.grad(FiniteDifferences.central_fdm(4, 1), f, x)[1] | ||
# TODO(mhauru) The Val(1) works around https://github.com/EnzymeAD/Enzyme.jl/issues/1807 | ||
@test( | ||
collect(Enzyme.gradient(Enzyme.Forward, Enzyme.Const(f), x, Val(1))) ≈ collect(finitediff), | ||
rtol = rtol, | ||
atol = atol | ||
) | ||
@test( | ||
Enzyme.gradient(Enzyme.Reverse, Enzyme.Const(f), x) ≈ finitediff, | ||
rtol = rtol, atol = atol | ||
) | ||
return nothing | ||
end | ||
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_sym(A) = A'A | ||
_pdmat(A) = PDMat(_sym(A) + 5I) | ||
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@testset "Distributions integration tests" begin | ||
# Distributions for which to test differentiating `logpdf(d, x)`. The first value of the | ||
# tuple is the `d`, the second is `x`. | ||
logpdf_test_cases = Any[ | ||
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# | ||
# Univariate | ||
# | ||
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(Arcsine(), 0.5), | ||
(Arcsine(-0.3, 0.9), 0.5), | ||
(Arcsine(0.5, 1.1), 1.0), | ||
(Beta(1.1, 1.1), 0.5), | ||
(Beta(1.1, 1.5), 0.9), | ||
(Beta(1.6, 1.5), 0.5), | ||
(BetaPrime(1.1, 1.1), 0.5), | ||
(BetaPrime(1.1, 1.6), 0.5), | ||
(BetaPrime(1.6, 1.3), 0.9), | ||
(Biweight(1.0, 2.0), 0.5), | ||
(Biweight(-0.5, 2.5), -0.45), | ||
(Biweight(0.0, 1.0), 0.3), | ||
(Cauchy(), -0.5), | ||
(Cauchy(1.0), 0.99), | ||
(Cauchy(1.0, 0.1), 1.01), | ||
(Chi(2.5), 0.5), | ||
(Chi(5.5), 1.1), | ||
(Chi(0.1), 0.7), | ||
(Chisq(2.5), 0.5), | ||
(Chisq(5.5), 1.1), | ||
(Chisq(0.1), 0.7), | ||
(Cosine(0.0, 1.0), 0.5), | ||
(Cosine(-0.5, 2.0), -0.1), | ||
(Cosine(0.4, 0.5), 0.0), | ||
(Epanechnikov(0.0, 1.0), 0.5), | ||
(Epanechnikov(-0.5, 1.2), -0.9), | ||
(Epanechnikov(-0.4, 1.6), 0.1), | ||
(Erlang(), 0.5), | ||
(Erlang(), 0.1), | ||
(Erlang(), 0.9), | ||
(Exponential(), 0.1), | ||
(Exponential(0.5), 0.9), | ||
(Exponential(1.4), 0.05), | ||
(FDist(2.1, 3.5), 0.7), | ||
(FDist(1.4, 5.4), 3.5), | ||
(FDist(5.5, 3.3), 7.2), | ||
(Frechet(), 0.1), | ||
(Frechet(), 1.1), | ||
(Frechet(1.5, 2.4), 0.1), | ||
(Gamma(0.9, 1.2), 4.5), | ||
(Gamma(0.5, 1.9), 1.5), | ||
(Gamma(1.8, 3.2), 1.0), | ||
(GeneralizedExtremeValue(0.3, 1.3, 0.1), 2.4), | ||
(GeneralizedExtremeValue(-0.7, 2.2, 0.4), 1.1), | ||
(GeneralizedExtremeValue(0.5, 0.9, -0.5), -7.0), | ||
(GeneralizedPareto(0.3, 1.1, 1.1), 5.0), | ||
(GeneralizedPareto(-0.25, 0.9, 0.1), 0.8), | ||
(GeneralizedPareto(0.3, 1.1, -5.1), 0.31), | ||
(Gumbel(0.1, 0.5), 0.1), | ||
(Gumbel(-0.5, 1.1), -0.1), | ||
(Gumbel(0.3, 0.1), 0.3), | ||
(InverseGaussian(0.1, 0.5), 1.1), | ||
(InverseGaussian(0.2, 1.1), 3.2), | ||
(InverseGaussian(0.1, 1.2), 0.5), | ||
(JohnsonSU(0.1, 0.95, 0.1, 1.1), 0.1), | ||
(JohnsonSU(0.15, 0.9, 0.12, 0.94), 0.5), | ||
(JohnsonSU(0.1, 0.95, 0.1, 1.1), -0.3), | ||
(Kolmogorov(), 1.1), | ||
(Kolmogorov(), 0.9), | ||
(Kolmogorov(), 1.5), | ||
(Kumaraswamy(2.0, 5.0), 0.71), | ||
(Kumaraswamy(0.1, 5.0), 0.2), | ||
(Kumaraswamy(0.5, 4.5), 0.1), | ||
(Laplace(0.1, 1.0), 0.2), | ||
(Laplace(-0.5, 2.1), 0.5), | ||
(Laplace(-0.35, 0.4), -0.3), | ||
(Levy(0.1, 0.9), 4.1), | ||
(Levy(0.5, 0.9), 0.6), | ||
(Levy(1.1, 0.5), 2.2), | ||
(Lindley(0.5), 2.1), | ||
(Lindley(1.1), 3.1), | ||
(Lindley(1.9), 3.5), | ||
(Logistic(0.1, 1.2), 1.1), | ||
(Logistic(0.5, 0.7), 0.6), | ||
(Logistic(-0.5, 0.1), -0.4), | ||
(LogitNormal(0.1, 1.1), 0.5), | ||
(LogitNormal(0.5, 0.7), 0.6), | ||
(LogitNormal(-0.12, 1.1), 0.1), | ||
(LogNormal(0.0, 1.0), 0.5), | ||
(LogNormal(0.5, 1.0), 0.5), | ||
(LogNormal(-0.1, 1.3), 0.75), | ||
(LogUniform(0.1, 0.9), 0.75), | ||
(LogUniform(0.15, 7.8), 7.1), | ||
(LogUniform(2.0, 3.0), 2.1), | ||
# (NoncentralBeta(1.1, 1.1, 1.2), 0.8), # foreigncall (Rmath.dnbeta). | ||
# (NoncentralChisq(2, 3.0), 10.0), # foreigncall (Rmath.dnchisq). | ||
# (NoncentralF(2, 3, 1.1), 4.1), # foreigncall (Rmath.dnf). | ||
# (NoncentralT(1.3, 1.1), 0.1), # foreigncall (Rmath.dnt). | ||
(Normal(), 0.1), | ||
(Normal(0.0, 1.0), 1.0), | ||
(Normal(0.5, 1.0), 0.05), | ||
(Normal(0.0, 1.5), -0.1), | ||
(Normal(-0.1, 0.9), -0.3), | ||
# (NormalInverseGaussian(0.0, 1.0, 0.2, 0.1), 0.1), # foreigncall -- https://github.com/JuliaMath/SpecialFunctions.jl/blob/be1fa06fee58ec019a28fb0cd2b847ca83a5af9a/src/bessel.jl#L265 | ||
(Pareto(1.0, 1.0), 3.5), | ||
(Pareto(1.1, 0.9), 3.1), | ||
(Pareto(1.0, 1.0), 1.4), | ||
(PGeneralizedGaussian(0.2), 5.0), | ||
(PGeneralizedGaussian(0.5, 1.0, 0.3), 5.0), | ||
(PGeneralizedGaussian(-0.1, 11.1, 6.5), -0.3), | ||
(Rayleigh(0.5), 0.6), | ||
(Rayleigh(0.9), 1.1), | ||
(Rayleigh(0.55), 0.63), | ||
# (Rician(0.5, 1.0), 2.1), # foreigncall (Rmath.dnchisq). Not implemented anywhere. | ||
(Semicircle(1.0), 0.9), | ||
(Semicircle(5.1), 5.05), | ||
(Semicircle(0.5), -0.1), | ||
(SkewedExponentialPower(0.1, 1.0, 0.97, 0.7), -2.0), | ||
(SkewedExponentialPower(0.15, 1.0, 0.97, 0.7), -2.0), | ||
(SkewedExponentialPower(0.1, 1.1, 0.99, 0.7), 0.5), | ||
(SkewNormal(0.0, 1.0, -1.0), 0.1), | ||
(SkewNormal(0.5, 2.0, 1.1), 0.1), | ||
(SkewNormal(-0.5, 1.0, 0.0), 0.1), | ||
(SymTriangularDist(0.0, 1.0), 0.5), | ||
(SymTriangularDist(-0.5, 2.1), -2.0), | ||
(SymTriangularDist(1.7, 0.3), 1.75), | ||
(TDist(1.1), 99.1), | ||
(TDist(10.1), 25.0), | ||
(TDist(2.1), -89.5), | ||
(TriangularDist(0.0, 1.5, 0.5), 0.45), | ||
(TriangularDist(0.1, 1.4, 0.45), 0.12), | ||
(TriangularDist(0.0, 1.5, 0.5), 0.2), | ||
(Triweight(1.0, 1.0), 1.0), | ||
(Triweight(1.1, 2.1), 1.0), | ||
(Triweight(1.9, 10.0), -0.1), | ||
(Uniform(0.0, 1.0), 0.2), | ||
(Uniform(-0.1, 1.1), 1.0), | ||
(Uniform(99.5, 100.5), 100.0), | ||
(VonMises(0.5), 0.1), | ||
(VonMises(0.3), -0.1), | ||
(VonMises(0.2), -0.5), | ||
(Weibull(0.5, 1.0), 0.45), | ||
(Weibull(0.3, 1.1), 0.66), | ||
(Weibull(0.75, 1.3), 0.99), | ||
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# | ||
# Multivariate | ||
# | ||
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(MvNormal(1, 1.5), [-0.3]), | ||
(MvNormal(2, 0.5), [0.2, -0.3]), | ||
(MvNormal([1.0]), [-0.1]), | ||
(MvNormal([1.0, 0.9]), [-0.1, -0.7]), | ||
(MvNormal([0.0], 0.9), [0.1]), | ||
(MvNormal([0.0, 0.1], 0.9), [0.1, -0.05]), | ||
(MvNormal(Diagonal([0.1])), [0.1]), | ||
(MvNormal(Diagonal([0.1, 0.2])), [0.1, 0.15]), | ||
(MvNormal([0.1, -0.3], Diagonal(Fill(0.9, 2))), [0.1, -0.1]), | ||
(MvNormal([0.1, -0.1], 0.4I), [-0.1, 0.15]), | ||
(MvNormal([0.2, 0.3], Hermitian(Diagonal([0.5, 0.4]))), [-0.1, 0.05]), | ||
(MvNormal([0.2, 0.3], Symmetric(Diagonal([0.5, 0.4]))), [-0.1, 0.05]), | ||
(MvNormal([0.2, 0.3], Diagonal([0.5, 0.4])), [-0.1, 0.05]), | ||
(MvNormal([-0.15], _pdmat([1.1]')), [-0.05]), | ||
(MvNormal([0.2, -0.15], _pdmat([1.0 0.9; 0.7 1.1])), [0.05, -0.05]), | ||
(MvNormal([0.2, -0.3], [0.5, 0.6]), [0.4, -0.3]), | ||
(MvNormalCanon([0.1, -0.1], _pdmat([0.5 0.4; 0.45 1.0])), [0.2, -0.25]), | ||
(MvLogNormal(MvNormal([0.2, -0.1], _pdmat([1.0 0.9; 0.7 1.1]))), [0.5, 0.1]), | ||
(product_distribution([Normal()]), [0.3]), | ||
(product_distribution([Normal(), Uniform()]), [-0.4, 0.3]), | ||
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# | ||
# Matrix-variate | ||
# | ||
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( | ||
MatrixNormal( | ||
randn(2, 3), _pdmat(randn(2, 2)), _pdmat(randn(3, 3)) | ||
), | ||
randn(2, 3), | ||
), | ||
( | ||
Wishart(5, _pdmat(randn(3, 3))), | ||
Symmetric(collect(_pdmat(randn(3, 3)))), | ||
), | ||
( | ||
InverseWishart(5, _pdmat(randn(3, 3))), | ||
Symmetric(collect(_pdmat(randn(3, 3)))), | ||
), | ||
( | ||
MatrixTDist( | ||
3.1, | ||
randn(2, 3), | ||
_pdmat(randn(2, 2)), | ||
_pdmat(randn(3, 3)), | ||
), | ||
randn(2, 3), | ||
), | ||
(MatrixBeta(5, 6.0, 7.0), rand(MatrixBeta(5, 6.0, 6.0))), | ||
( | ||
MatrixFDist(6.0, 7.0, _pdmat(randn(5, 5))), | ||
rand(MatrixFDist(6.0, 7.0, _pdmat(randn(5, 5)))), | ||
), | ||
(LKJ(5, 1.1), rand(LKJ(5, 1.1))), | ||
] | ||
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# Cases where the function to differentiate isn't just straight up `logpdf(d, x)`. | ||
# Values in the tuple are (name, function to differentiate, value to differentiate at). | ||
work_around_test_cases = Any[ | ||
("InverseGamma", (a, b, x) -> logpdf(InverseGamma(a, b), x), (1.5, 1.4, 0.4)), | ||
("NormalCanon", (m, s, x) -> logpdf(NormalCanon(m, s), x), (0.1, 1.0, -0.5)), | ||
("Categorical", x -> logpdf(Categorical(x, 1 - x), 1), 0.3), | ||
( | ||
"MvLogitNormal", | ||
(m, S, x) -> logpdf(MvLogitNormal(m, S), vcat(x, 1 - sum(x))), | ||
([0.4, 0.6], Symmetric(_pdmat([0.9 0.4; 0.5 1.1])), [0.27, 0.24]), | ||
), | ||
( | ||
"truncated Beta", | ||
(a, b, α, β, x) -> logpdf(truncated(Beta(α, β), a, b), x), | ||
(0.1, 0.9, 1.1, 1.3, 0.4), | ||
), | ||
( | ||
"allocs Normal", | ||
(a, b, x) -> logpdf(truncated(Normal(), a, b), x), | ||
(-0.3, 0.3, 0.1), | ||
), | ||
( | ||
"allocs Uniform", | ||
(a, b, α, β, x) -> logpdf(truncated(Uniform(α, β), a, b), x), | ||
(0.1, 0.9, -0.1, 1.1, 0.4), | ||
), | ||
("Dirichlet", (a, x) -> logpdf(Dirichlet(a), [x, 1-x]), ([1.5, 1.1], 0.6)), | ||
( | ||
"reshape", | ||
x -> logpdf(reshape(product_distribution([Normal(), Uniform()]), 1, 2), x), | ||
([2.1 0.7],), | ||
), | ||
("vec", x -> logpdf(vec(LKJ(2, 1.1)), x), ([1.0, 0.489, 0.489, 1.0],)), | ||
( | ||
"LKJCholesky", | ||
function(X, v) | ||
# LKJCholesky distributes over the Cholesky factorisation of correlation | ||
# matrices, so the argument to `logpdf` must be such a matrix. | ||
S = X'X | ||
Λ = Diagonal(map(inv ∘ sqrt, diag(S))) | ||
C = cholesky(Symmetric(Λ * S * Λ)) | ||
return logpdf(LKJCholesky(2, v), C) | ||
end, | ||
(randn(2, 2), 1.1), | ||
), | ||
] | ||
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@testset "$(nameof(typeof(d)))" for (d, x) in logpdf_test_cases | ||
test_grad(x -> logpdf(d, x), x) | ||
end | ||
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@testset "$name" for (name, f, x) in work_around_test_cases | ||
test_grad(y -> f(y...), x) | ||
end | ||
end | ||
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end |
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