Extension of #269: Use \circ and compose and deprecate transform (

#276)

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: kaandocal <>

Project.toml

@@ -1,10 +1,11 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.9.1"
+version = "0.9.2"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
+CompositionsBase = "a33af91c-f02d-484b-be07-31d278c5ca2b"
 Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -20,6 +21,7 @@ ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"
 [compat]
 ChainRulesCore = "0.9"
 Compat = "3.7"
+CompositionsBase = "0.1"
 Distances = "0.10"
 Functors = "0.1"
 Requires = "1.0.1"

docs/create_kernel_plots.jl

@@ -13,7 +13,7 @@ n_grid = 101
 fill(x₀, n_grid, 1)
 xrange = reshape(collect(range(-3, 3; length=n_grid)), :, 1)
 
-k = transform(SqExponentialKernel(), 1.0)
+k = SqExponentialKernel() ∘ ScaleTransform(1.0)
 K1 = kernelmatrix(k, xrange; obsdim=1)
 p = heatmap(
     K1;
@@ -35,7 +35,7 @@ p = heatmap(
 )
 savefig(joinpath(@__DIR__, "src", "assets", "heatmap_matern.png"))
 
-k = transform(PolynomialKernel(; c=0.0, d=2.0), LinearTransform(randn(3, 1)))
+k = PolynomialKernel(; c=0.0, d=2.0) ∘ LinearTransform(randn(3, 1))
 K3 = kernelmatrix(k, xrange; obsdim=1)
 p = heatmap(
     K3;
@@ -47,7 +47,7 @@ p = heatmap(
 savefig(joinpath(@__DIR__, "src", "assets", "heatmap_poly.png"))
 
 k =
-    0.5 * SqExponentialKernel() * transform(LinearKernel(), 0.5) +
+    0.5 * SqExponentialKernel() * (LinearKernel() ∘ ScaleTransform(0.5)) +
     0.4 * (@kernel Matern32Kernel() FunctionTransform(x -> sin.(x)))
 K4 = kernelmatrix(k, xrange; obsdim=1)
 p = heatmap(

docs/src/kernels.md

@@ -118,9 +118,7 @@ of kernels together.
 
 ```@docs
 TransformedKernel
-transform(::Kernel, ::Transform)
-transform(::Kernel, ::Real)
-transform(::Kernel, ::AbstractVector)
+∘(::Kernel, ::Transform)
 ScaledKernel
 KernelSum
 KernelProduct

docs/src/transform.md

@@ -18,8 +18,8 @@ LowRankTransform(rand(10, 5)) ∘ ScaleTransform(2.0)
 A transformation `t` can be applied to a single input `x` with `t(x)` and to multiple inputs
 `xs` with `map(t, xs)`.
 
-Kernels can be coupled with input transformations with
-[`transform`](@ref). It falls back to creating a [`TransformedKernel`](@ref) but allows more
+Kernels can be coupled with input transformations with [`∘`](@ref) or its alias `compose`. It falls
+back to creating a [`TransformedKernel`](@ref) but allows more
 optimized implementations for specific kernels and transformations.
 
 ## List of Input Transforms

src/KernelFunctions.jl

@@ -39,11 +39,12 @@ export MOInput
 export IndependentMOKernel, LatentFactorMOKernel
 
 # Reexports
-export tensor, ⊗
+export tensor, ⊗, compose
 
 using Compat
 using ChainRulesCore: ChainRulesCore, Composite, Zero, One, DoesNotExist, NO_FIELDS
 using ChainRulesCore: @thunk, InplaceableThunk
+using CompositionsBase
 using Requires
 using Distances, LinearAlgebra
 using Functors
@@ -106,6 +107,8 @@ include("zygoterules.jl")
 
 include("test_utils.jl")
 
+include("deprecations.jl")
+
 function __init__()
     @require Kronecker = "2c470bb0-bcc8-11e8-3dad-c9649493f05e" begin
         include(joinpath("matrix", "kernelkroneckermat.jl"))

src/basekernels/gabor.jl

@@ -14,8 +14,11 @@ k(x, x'; l, p) = \\exp\\bigg(- \\cos\\bigg(\\pi\\sum_{i=1}^d \\frac{x_i - x'_i}{
 """
 struct GaborKernel{K<:Kernel} <: Kernel
     kernel::K
+
     function GaborKernel(; ell=nothing, p=nothing)
-        k = _gabor(; ell=ell, p=p)
+        ell_transform = _lengthscale_transform(ell)
+        p_transform = _lengthscale_transform(p)
+        k = (SqExponentialKernel() ∘ ell_transform) * (CosineKernel() ∘ p_transform)
         return new{typeof(k)}(k)
     end
 end
@@ -24,38 +27,23 @@ end
 
 (κ::GaborKernel)(x, y) = κ.kernel(x, y)
 
-function _gabor(; ell=nothing, p=nothing)
-    if ell === nothing
-        if p === nothing
-            return SqExponentialKernel() * CosineKernel()
-        else
-            return SqExponentialKernel() * transform(CosineKernel(), 1 ./ p)
-        end
-    elseif p === nothing
-        return transform(SqExponentialKernel(), 1 ./ ell) * CosineKernel()
-    else
-        return transform(SqExponentialKernel(), 1 ./ ell) *
-               transform(CosineKernel(), 1 ./ p)
-    end
-end
+_lengthscale_transform(::Nothing) = IdentityTransform()
+_lengthscale_transform(x::Real) = ScaleTransform(inv(x))
+_lengthscale_transform(x::AbstractVector) = ARDTransform(map(inv, x))
+
+_lengthscale(::IdentityTransform) = 1
+_lengthscale(t::ScaleTransform) = inv(first(t.s))
+_lengthscale(t::ARDTransform) = map(inv, t.v)
 
 function Base.getproperty(k::GaborKernel, v::Symbol)
     if v == :kernel
         return getfield(k, v)
     elseif v == :ell
-        kernel1 = k.kernel.kernels[1]
-        if kernel1 isa TransformedKernel
-            return 1 ./ kernel1.transform.s[1]
-        else
-            return 1.0
-        end
+        ell_transform = k.kernel.kernels[1].transform
+        return _lengthscale(ell_transform)
     elseif v == :p
-        kernel2 = k.kernel.kernels[2]
-        if kernel2 isa TransformedKernel
-            return 1 ./ kernel2.transform.s[1]
-        else
-            return 1.0
-        end
+        p_transform = k.kernel.kernels[2].transform
+        return _lengthscale(p_transform)
     else
         error("Invalid Property")
     end

src/deprecations.jl

@@ -0,0 +1,4 @@
+@deprecate transform(k::Kernel, t::Transform) k ∘ t
+@deprecate transform(k::TransformedKernel, t::Transform) k.kernel ∘ t ∘ k.transform
+@deprecate transform(k::Kernel, ρ::Real) k ∘ ScaleTransform(ρ)
+@deprecate transform(k::Kernel, ρ::AbstractVector) k ∘ ARDTransform(ρ)

src/kernels/transformedkernel.jl

@@ -3,17 +3,11 @@
 
 Kernel derived from `k` for which inputs are transformed via a [`Transform`](@ref) `t`.
 
-It is preferred to create kernels with input transformations with [`transform`](@ref)
-instead of  `TransformedKernel` directly since [`transform`](@ref) allows optimized
-implementations for specific kernels and transformations.
+The preferred way to create kernels with input transformations is to use the composition
+operator [`∘`](@ref) or its alias `compose` instead of `TransformedKernel` directly since
+this allows optimized implementations for specific kernels and transformations.
 
-# Definition
-
-For inputs ``x, x'``, the transformed kernel ``\\widetilde{k}`` derived from kernel ``k`` by
-input transformation ``t`` is defined as
-```math
-\\widetilde{k}(x, x'; k, t) = k\\big(t(x), t(x')\\big).
-```
+See also: [`∘`](@ref)
 """
 struct TransformedKernel{Tk<:Kernel,Tr<:Transform} <: Kernel
     kernel::Tk
@@ -42,30 +36,37 @@ end
 _scale(t::ScaleTransform, metric, x, y) = evaluate(metric, t(x), t(y))
 
 """
-    transform(k::Kernel, t::Transform)
+    kernel ∘ transform
+    ∘(kernel, transform)
+    compose(kernel, transform)
 
-Create a [`TransformedKernel`](@ref) for kernel `k` and transform `t`.
-"""
-transform(k::Kernel, t::Transform) = TransformedKernel(k, t)
-function transform(k::TransformedKernel, t::Transform)
-    return TransformedKernel(k.kernel, t ∘ k.transform)
-end
+Compose a `kernel` with a transformation `transform` of its inputs.
 
-"""
-    transform(k::Kernel, ρ::Real)
+The prefix forms support chains of multiple transformations:
+`∘(kernel, transform1, transform2) = kernel ∘ transform1 ∘ transform2`.
 
-Create a [`TransformedKernel`](@ref) for kernel `k` and inverse lengthscale `ρ`.
-"""
-transform(k::Kernel, ρ::Real) = transform(k, ScaleTransform(ρ))
+# Definition
 
-"""
-    transform(k::Kernel, ρ::AbstractVector)
+For inputs ``x, x'``, the transformed kernel ``\\widetilde{k}`` derived from kernel ``k`` by
+input transformation ``t`` is defined as
+```math
+\\widetilde{k}(x, x'; k, t) = k\\big(t(x), t(x')\\big).
+```
 
-Create a [`TransformedKernel`](@ref) for kernel `k` and inverse lengthscales `ρ`.
-"""
-transform(k::Kernel, ρ::AbstractVector) = transform(k, ARDTransform(ρ))
+# Examples
+
+```jldoctest
+julia> (SqExponentialKernel() ∘ ScaleTransform(0.5))(0, 2) == exp(-0.5)
+true
 
-kernel(κ) = κ.kernel
+julia> ∘(ExponentialKernel(), ScaleTransform(2), ScaleTransform(0.5))(1, 2) == exp(-1)
+true
+```
+
+See also: [`TransformedKernel`](@ref)
+"""
+Base.:∘(k::Kernel, t::Transform) = TransformedKernel(k, t)
+Base.:∘(k::TransformedKernel, t::Transform) = TransformedKernel(k.kernel, k.transform ∘ t)
 
 Base.show(io::IO, κ::TransformedKernel) = printshifted(io, κ, 0)
 
@@ -87,13 +88,13 @@ function kernelmatrix_diag!(
 end
 
 function kernelmatrix!(K::AbstractMatrix, κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix!(K, kernel(κ), _map(κ.transform, x))
+    return kernelmatrix!(K, κ.kernel, _map(κ.transform, x))
 end
 
 function kernelmatrix!(
     K::AbstractMatrix, κ::TransformedKernel, x::AbstractVector, y::AbstractVector
 )
-    return kernelmatrix!(K, kernel(κ), _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix!(K, κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
 end
 
 function kernelmatrix_diag(κ::TransformedKernel, x::AbstractVector)
@@ -105,9 +106,9 @@ function kernelmatrix_diag(κ::TransformedKernel, x::AbstractVector, y::Abstract
 end
 
 function kernelmatrix(κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix(kernel(κ), _map(κ.transform, x))
+    return kernelmatrix(κ.kernel, _map(κ.transform, x))
 end
 
 function kernelmatrix(κ::TransformedKernel, x::AbstractVector, y::AbstractVector)
-    return kernelmatrix(kernel(κ), _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix(κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
 end

test/basekernels/gabor.jl

@@ -10,14 +10,14 @@
     k_manual = exp(-sqeuclidean(v1, v2) / (2 * k.ell^2)) * cospi(euclidean(v1, v2) / k.p)
     @test k(v1, v2) ≈ k_manual atol = 1e-5
 
-    lhs_manual = transform(SqExponentialKernel(), 1 / k.ell)(v1, v2)
-    rhs_manual = transform(CosineKernel(), 1 / k.p)(v1, v2)
+    lhs_manual = (SqExponentialKernel() ∘ ScaleTransform(1 / k.ell))(v1, v2)
+    rhs_manual = (CosineKernel() ∘ ScaleTransform(1 / k.p))(v1, v2)
     @test k(v1, v2) ≈ lhs_manual * rhs_manual atol = 1e-5
 
     k = GaborKernel()
     @test k.ell ≈ 1.0 atol = 1e-5
     @test k.p ≈ 1.0 atol = 1e-5
-    @test repr(k) == "Gabor Kernel (ell = 1.0, p = 1.0)"
+    @test repr(k) == "Gabor Kernel (ell = 1, p = 1)"
 
     test_interface(k, Vector{Float64})
 

test/deprecations.jl

@@ -0,0 +1,20 @@
+@testset "deprecations.jl" begin
+    p = rand()
+    v = rand(3)
+    M = rand(3, 3)
+    v1 = rand(3)
+    v2 = rand(3)
+    kernel = SqExponentialKernel()
+
+    k1 = @test_deprecated transform(kernel, LinearTransform(M))
+    @test k1(v1, v2) == (kernel ∘ LinearTransform(M))(v1, v2)
+
+    k2 = @test_deprecated transform(kernel ∘ ScaleTransform(p), ARDTransform(v))
+    @test k2(v1, v2) == (kernel ∘ ARDTransform(v) ∘ ScaleTransform(p))(v1, v2)
+
+    k3 = @test_deprecated transform(kernel, p)
+    @test k3(v1, v2) == (kernel ∘ ScaleTransform(p))(v1, v2)
+
+    k4 = @test_deprecated transform(kernel, v)
+    @test k4(v1, v2) == (kernel ∘ ARDTransform(v))(v1, v2)
+end

test/kernels/transformedkernel.jl

@@ -5,26 +5,27 @@
     v2 = rand(rng, 3)
 
     s = rand(rng)
-    s2 = rand(rng)
     v = rand(rng, 3)
+    P = rand(rng, 3, 2)
     k = SqExponentialKernel()
     kt = TransformedKernel(k, ScaleTransform(s))
     ktard = TransformedKernel(k, ARDTransform(v))
-    @test kt(v1, v2) == transform(k, ScaleTransform(s))(v1, v2)
-    @test kt(v1, v2) == transform(k, s)(v1, v2)
+    @test kt(v1, v2) == (k ∘ ScaleTransform(s))(v1, v2)
     @test kt(v1, v2) ≈ k(s * v1, s * v2) atol = 1e-5
-    @test ktard(v1, v2) ≈ transform(k, ARDTransform(v))(v1, v2) atol = 1e-5
-    @test ktard(v1, v2) == transform(k, v)(v1, v2)
+    @test ktard(v1, v2) == (k ∘ ARDTransform(v))(v1, v2)
     @test ktard(v1, v2) == k(v .* v1, v .* v2)
-    @test transform(kt, s2)(v1, v2) ≈ kt(s2 * v1, s2 * v2)
-    @test KernelFunctions.kernel(kt) == k
+    @test (k ∘ LinearTransform(P') ∘ ScaleTransform(s))(v1, v2) ==
+          ((k ∘ LinearTransform(P')) ∘ ScaleTransform(s))(v1, v2) ==
+          (k ∘ (LinearTransform(P') ∘ ScaleTransform(s)))(v1, v2)
+
     @test repr(kt) == repr(k) * "\n\t- " * repr(ScaleTransform(s))
 
     TestUtils.test_interface(k, Float64)
-    test_ADs(x -> transform(SqExponentialKernel(), x[1]), rand(1))# ADs = [:ForwardDiff, :ReverseDiff])
+    test_ADs(x -> SqExponentialKernel() ∘ ScaleTransform(x[1]), rand(1))
+
     # Test implicit gradients
     @testset "Implicit gradients" begin
-        k = transform(SqExponentialKernel(), 2.0)
+        k = SqExponentialKernel() ∘ ScaleTransform(2.0)
         ps = Flux.params(k)
         X = rand(10, 1)
         x = vec(X)
@@ -46,12 +47,14 @@
         @test g1[first(ps)] ≈ g3[first(ps)]
     end
 
-    P = rand(3, 2)
-    c = Chain(Dense(3, 2))
+    @testset "Parameters" begin
+        k = ConstantKernel(; c=rand(rng))
+        c = Chain(Dense(3, 2))
 
-    test_params(transform(k, s), (k, [s]))
-    test_params(transform(k, v), (k, v))
-    test_params(transform(k, LinearTransform(P)), (k, P))
-    test_params(transform(k, LinearTransform(P) ∘ ScaleTransform(s)), (k, [s], P))
-    test_params(transform(k, FunctionTransform(c)), (k, c))
+        test_params(k ∘ ScaleTransform(s), (k, [s]))
+        test_params(k ∘ ARDTransform(v), (k, v))
+        test_params(k ∘ LinearTransform(P), (k, P))
+        test_params(k ∘ LinearTransform(P) ∘ ScaleTransform(s), (k, [s], P))
+        test_params(k ∘ FunctionTransform(c), (k, c))
+    end
 end

test/runtests.jl

@@ -148,6 +148,8 @@ include("test_utils.jl")
     include("chainrules.jl")
     include("zygoterules.jl")
 
+    include("deprecations.jl")
+
     @testset "doctests" begin
         DocMeta.setdocmeta!(
             KernelFunctions,

test/transform/ardtransform.jl

@@ -42,5 +42,5 @@
     @test_throws DimensionMismatch map(t, ColVecs(randn(rng, D + 1, 3)))
 
     @test repr(t) == "ARD Transform (dims: $D)"
-    test_ADs(x -> transform(SEKernel(), exp.(x)), randn(rng, 3))
+    test_ADs(x -> SEKernel() ∘ ARDTransform(exp.(x)), randn(rng, 3))
 end

test/transform/chaintransform.jl

@@ -23,7 +23,7 @@
     # Verify printing works as expected.
     @test repr(tp ∘ tf) == "Chain of 2 transforms:\n\t - $(tf) |> $(tp)"
     test_ADs(
-        x -> transform(SEKernel(), ScaleTransform(exp(x[1])) ∘ ARDTransform(exp.(x[2:4]))),
+        x -> SEKernel() ∘ (ScaleTransform(exp(x[1])) ∘ ARDTransform(exp.(x[2:4]))),
         randn(rng, 4),
     )
 end

test/transform/functiontransform.jl

@@ -28,5 +28,5 @@
 
     @test repr(FunctionTransform(sin)) == "Function Transform: $(sin)"
     f(a, x) = sin.(a .* x)
-    test_ADs(x -> transform(SEKernel(), FunctionTransform(y -> f(x, y))), randn(rng, 3))
+    test_ADs(x -> SEKernel() ∘ FunctionTransform(y -> f(x, y)), randn(rng, 3))
 end