Add variate transport

Author: oschulz

Project.toml

@@ -1,14 +1,17 @@
 name = "MeasureBase"
 uuid = "fa1605e6-acd5-459c-a1e6-7e635759db14"
 authors = ["Chad Scherrer <[email protected]> and contributors"]
-version = "0.10.0"
+version = "0.11.0"
 
 [deps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 IfElse = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
+InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
 IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
@@ -24,11 +27,14 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Tricks = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
 
 [compat]
+ChainRulesCore = "1"
+ChangesOfVariables = "0.1.3"
 Compat = "3.35, 4"
 ConstructionBase = "1.3"
 DensityInterface = "0.4"
 FillArrays = "0.12, 0.13"
 IfElse = "0.1"
+InverseFunctions = "0.1.7"
 IrrationalConstants = "0.1"
 LogExpFunctions = "0.3"
 LogarithmicNumbers = "1"
@@ -42,6 +48,7 @@ julia = "1.3"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 
 [targets]
-test = ["Aqua"]
+test = ["Aqua", "ChainRulesTestUtils"]

src/MeasureBase.jl

@@ -1,5 +1,7 @@
 module MeasureBase
 
+using Base: @propagate_inbounds
+
 using Random
 import Random: rand!
 import Random: gentype
@@ -11,13 +13,17 @@ import DensityInterface: densityof
 import DensityInterface: DensityKind
 using DensityInterface
 
+using InverseFunctions
+using ChangesOfVariables
+
 import Base.iterate
 import ConstructionBase
 using ConstructionBase: constructorof
 
 using PrettyPrinting
 const Pretty = PrettyPrinting
 
+using ChainRulesCore
 using FillArrays
 using Static
 
@@ -32,20 +38,11 @@ export logdensity_def
 export basemeasure
 export basekernel
 export productmeasure
-
-"""
-    inssupport(m, x)
-    insupport(m)
-
-`insupport(m,x)` computes whether `x` is in the support of `m`.
-
-`insupport(m)` returns a function, and satisfies
-
-    insupport(m)(x) == insupport(m, x)
-"""
-function insupport end
-
 export insupport
+export getdof
+export transport_to
+
+include("insupport.jl")
 
 abstract type AbstractMeasure end
 
@@ -63,7 +60,7 @@ gentype(μ::AbstractMeasure) = typeof(testvalue(μ))
 # gentype(μ::AbstractMeasure) = gentype(basemeasure(μ))
 
 using NaNMath
-using LogExpFunctions: logsumexp
+using LogExpFunctions: logsumexp, logistic, logit
 
 @deprecate instance_type(x) Core.Typeof(x) false
 
@@ -94,6 +91,8 @@ using Compat
 
 using IrrationalConstants
 
+include("getdof.jl")
+include("transport.jl")
 include("schema.jl")
 include("splat.jl")
 include("proxies.jl")
@@ -125,9 +124,9 @@ include("combinators/powerweighted.jl")
 include("combinators/conditional.jl")
 
 include("standard/stdmeasure.jl")
-include("standard/stdnormal.jl")
 include("standard/stduniform.jl")
 include("standard/stdexponential.jl")
+include("standard/stdlogistic.jl")
 
 include("rand.jl")
 

src/combinators/power.jl

@@ -85,6 +85,13 @@ end
     end
 end
 
+@inline function logdensity_def(
+    d::PowerMeasure{M,NTuple{N, Base.OneTo{StaticInt{0}}}},
+    x,
+) where {M,N}
+    static(0.0)
+end
+
 @inline function insupport(μ::PowerMeasure, x)
     p = μ.parent
     all(x) do xj
@@ -100,3 +107,24 @@ end
         dynamic(insupport(p, xj))
     end
 end
+
+
+@inline getdof(μ::PowerMeasure) = getdof(μ.parent) * prod(map(length, μ.axes))
+
+@inline getdof(::PowerMeasure{<:Any, NTuple{N,Base.OneTo{StaticInt{0}}}}) where N = static(0)
+
+
+@propagate_inbounds function checked_var(μ::PowerMeasure, x::AbstractArray{<:Any})
+    @boundscheck begin
+        sz_μ = map(length, μ.axes)
+        sz_x = size(x)
+        if sz_μ != sz_x
+            throw(ArgumentError("Size of variate doesn't match size of power measure"))
+        end
+    end
+    return x
+end
+
+function checked_var(μ::PowerMeasure, x::Any)
+    throw(ArgumentError("Size of variate doesn't match size of power measure"))
+end

src/combinators/transformedmeasure.jl

@@ -13,3 +13,94 @@ function params(::AbstractTransformedMeasure) end
 function paramnames(::AbstractTransformedMeasure) end
 
 function parent(::AbstractTransformedMeasure) end
+
+
+export PushforwardMeasure
+
+"""
+    struct PushforwardMeasure{FF,IF,MU,VC<:TransformVolCorr} <: AbstractPushforward
+        f :: FF
+        inv_f :: IF
+        origin :: MU
+        volcorr :: VC
+    end
+"""
+struct PushforwardMeasure{FF,IF,M,VC<:TransformVolCorr} <: AbstractPushforward
+    f::FF
+    inv_f::IF
+    origin::M
+    volcorr::VC
+end
+
+gettransform(ν::PushforwardMeasure) = ν.f
+parent(ν::PushforwardMeasure) = ν.origin
+
+
+function Pretty.tile(ν::PushforwardMeasure)
+    Pretty.list_layout(Pretty.tile.([ν.f, ν.inv_f, ν.origin]); prefix = :PushforwardMeasure)
+end
+
+
+@inline function logdensity_def(ν::PushforwardMeasure{FF,IF,M,<:WithVolCorr}, y) where {FF,IF,M}
+    x_orig, inv_ladj = with_logabsdet_jacobian(ν.inv_f, y)
+    logd_orig = logdensity_def(ν.origin, x_orig)
+    logd = float(logd_orig + inv_ladj)
+    neginf = oftype(logd, -Inf)
+    return ifelse(
+        # Zero density wins against infinite volume:
+        (isnan(logd) && logd_orig == -Inf && inv_ladj == +Inf) ||
+        # Maybe  also for (logd_orig == -Inf) && isfinite(inv_ladj) ?
+        # Return constant -Inf to prevent problems with ForwardDiff:
+        (isfinite(logd_orig) && (inv_ladj == -Inf)),
+        neginf,
+        logd
+    )
+end
+
+@inline function logdensity_def(ν::PushforwardMeasure{FF,IF,M,<:NoVolCorr}, y) where {FF,IF,M}
+    x_orig = to_origin(ν, y)
+    return logdensity_def(ν.origin, x_orig)
+end
+
+
+insupport(ν::PushforwardMeasure, y) = insupport(transport_origin(ν), to_origin(ν, y))
+
+testvalue(ν::PushforwardMeasure) = from_origin(ν, testvalue(transport_origin(ν)))
+
+@inline function basemeasure(ν::PushforwardMeasure)
+    PushforwardMeasure(ν.f, ν.inv_f, basemeasure(transport_origin(ν)), NoVolCorr())
+end
+
+
+_pushfwd_dof(::Type{MU}, ::Type, dof) where MU = NoDOF{MU}()
+_pushfwd_dof(::Type{MU}, ::Type{<:Tuple{Any,Real}}, dof) where MU = dof
+
+# Assume that DOF are preserved if with_logabsdet_jacobian is functional:
+@inline function getdof(ν::MU) where {MU<:PushforwardMeasure}
+    T = Core.Compiler.return_type(testvalue, Tuple{typeof(ν.origin)})
+    R = Core.Compiler.return_type(with_logabsdet_jacobian, Tuple{typeof(ν.f), T})
+    _pushfwd_dof(MU, R, getdof(ν.origin))
+end
+
+# Bypass `checked_var`, would require potentially costly transformation:
+@inline checked_var(::PushforwardMeasure, x) = x
+
+
+@inline transport_origin(ν::PushforwardMeasure) = ν.origin
+@inline from_origin(ν::PushforwardMeasure, x) = ν.f(x)
+@inline to_origin(ν::PushforwardMeasure, y) = ν.inv_f(y)
+
+function Base.rand(rng::AbstractRNG, ::Type{T}, ν::PushforwardMeasure) where T
+    return from_origin(ν, rand(rng, T, transport_origin(ν)))
+end
+
+
+export pushfwd
+
+"""
+    pushfwd(f, μ, volcorr = WithVolCorr())
+
+Return the [pushforward measure](https://en.wikipedia.org/wiki/Pushforward_measure)
+from `μ` the [measurable function](https://en.wikipedia.org/wiki/Measurable_function) `f`.
+"""
+pushfwd(f, μ, volcorr = WithVolCorr()) = PushforwardMeasure(f, inverse(f), μ, volcorr)

src/combinators/weighted.jl

@@ -48,3 +48,7 @@ Base.:*(m::AbstractMeasure, k::Real) = k * m
 gentype(μ::WeightedMeasure) = gentype(μ.base)
 
 insupport(μ::WeightedMeasure, x) = insupport(μ.base, x)
+
+transport_origin(ν::WeightedMeasure) = ν.base
+to_origin(::WeightedMeasure, y) = y
+from_origin(::WeightedMeasure, x) = x

src/getdof.jl

@@ -0,0 +1,77 @@
+"""
+    MeasureBase.NoDOF{MU}
+
+Indicates that there is no way to compute degrees of freedom of a measure
+of type `MU` with the given information, e.g. because the DOF are not
+a global property of the measure.
+"""
+struct NoDOF{MU} end
+
+
+"""
+    getdof(μ)
+
+Returns the effective number of degrees of freedom of variates of
+measure `μ`.
+
+The effective NDOF my differ from the length of the variates. For example,
+the effective NDOF for a Dirichlet distribution with variates of length `n`
+is `n - 1`.
+
+Also see [`check_dof`](@ref).
+"""
+function getdof end
+
+# Prevent infinite recursion:
+@inline _default_getdof(::Type{MU}, ::MU) where MU = NoDOF{MU}
+@inline _default_getdof(::Type{MU}, mu_base) where MU = getdof(mu_base)
+
+@inline getdof(μ::MU) where MU = _default_getdof(MU, basemeasure(μ))
+
+
+"""
+    MeasureBase.check_dof(ν, μ)::Nothing
+
+Check if `ν` and `μ` have the same effective number of degrees of freedom
+according to [`MeasureBase.getdof`](@ref).
+"""
+function check_dof end
+
+function check_dof(ν, μ)
+    n_ν = getdof(ν)
+    n_μ = getdof(μ)
+    if n_ν != n_μ
+        throw(ArgumentError("Measure ν of type $(nameof(typeof(ν))) has $(n_ν) DOF but μ of type $(nameof(typeof(μ))) has $(n_μ) DOF"))
+    end
+    return nothing
+end
+
+_check_dof_pullback(ΔΩ) = NoTangent(), NoTangent(), NoTangent()
+ChainRulesCore.rrule(::typeof(check_dof), ν, μ) = check_dof(ν, μ), _check_dof_pullback
+
+
+"""
+    MeasureBase.NoVarCheck{MU,T}
+
+Indicates that there is no way to check of a values of type `T` are
+variate of measures of type `MU`.
+"""
+struct NoVarCheck{MU,T} end
+
+
+"""
+    MeasureBase.checked_var(μ::MU, x::T)::T
+
+Return `x` if `x` is a valid variate of `μ`, throw an `ArgumentError` if not,
+return `NoVarCheck{MU,T}()` if not check can be performed.
+"""
+function checked_var end
+
+# Prevent infinite recursion:
+@propagate_inbounds _default_checked_var(::Type{MU}, ::MU, ::T) where {MU,T} = NoVarCheck{MU,T}
+@propagate_inbounds _default_checked_var(::Type{MU}, mu_base, x) where MU = checked_var(mu_base, x)
+
+@propagate_inbounds checked_var(mu::MU, x) where MU = _default_checked_var(MU, basemeasure(mu), x)
+
+_checked_var_pullback(ΔΩ) = NoTangent(), NoTangent(), ΔΩ
+ChainRulesCore.rrule(::typeof(checked_var), ν, x) = checked_var(ν, x), _checked_var_pullback

src/insupport.jl

@@ -0,0 +1,32 @@
+"""
+    inssupport(m, x)
+    insupport(m)
+
+`insupport(m,x)` computes whether `x` is in the support of `m`.
+
+`insupport(m)` returns a function, and satisfies
+
+insupport(m)(x) == insupport(m, x)
+"""
+function insupport end
+
+
+"""
+    MeasureBase.require_insupport(μ, x)::Nothing
+
+Checks if `x` is in the support of distribution/measure `μ`, throws an
+`ArgumentError` if not.
+"""
+function require_insupport end
+
+_require_insupport_pullback(ΔΩ) = NoTangent(), ZeroTangent()
+function ChainRulesCore.rrule(::typeof(require_insupport), μ, x)
+    return require_insupport(μ, x), _require_insupport_pullback
+end
+
+function require_insupport(μ, x)
+    if !insupport(μ, x)
+        throw(ArgumentError("x is not within the support of μ"))
+    end
+    return nothing
+end