Add Latent-factor multi-output kernel

src/KernelFunctions.jl

@@ -31,7 +31,7 @@ export NystromFact, nystrom
 export spectral_mixture_kernel, spectral_mixture_product_kernel
 
 export MOInput
-export IndependentMOKernel
+export IndependentMOKernel, LatentFactorMOKernel
 
 using Compat
 using Requires
@@ -73,6 +73,7 @@ include("generic.jl")
 
 include("mokernels/moinput.jl")
 include("mokernels/independent.jl")
+include("mokernels/slfm.jl")
 
 include("zygote_adjoints.jl")
 

src/basekernels/periodic.jl

@@ -24,4 +24,4 @@ metric(κ::PeriodicKernel) = Sinus(κ.r)
 
 kappa(κ::PeriodicKernel, d::Real) = exp(- 0.5d)
 
-Base.show(io::IO, κ::PeriodicKernel) = print(io, "Periodic Kernel, length(r) = ", length(κ.r), ")")
+Base.show(io::IO, κ::PeriodicKernel) = print(io, "Periodic Kernel (length(r) = ", length(κ.r), ")")

src/mokernels/slfm.jl

@@ -0,0 +1,63 @@
+@doc raw"""
+    LatentFactorMOKernel(
+        g::AbstractVector{<:Kernel}, 
+        e::AbstractVector{<:Kernel}, 
+        A::AbstractMatrix
+        )
+
+A semiparametric kernel for problems involving multiple response variables.
+
+``k((x, p), (y, p)) = k_p(x, y) = \Sum^{Q}_{q=1} A_{pq}g_q(x, y) + e_p(x, y)``
+
+# Arguments
+- `g::AbstractVector{<:Kernel}`: an array of kernels
+- `e::AbstractVector{<:Kernel}`: an array of kernels
+- `A::AbstractMatrix`: an matrix of weights for the kernels of shape (length(e), length(g))
+
+
+# Reference:
+- [Seeger, Teh, and Jordan (2005)](https://infoscience.epfl.ch/record/161465/files/slfm-long.pdf)
+
+"""
+struct LatentFactorMOKernel{Tg, Te, TA <: AbstractMatrix} <: Kernel
+    g::Tg
+    e::Te
+    A::TA
+    function LatentFactorMOKernel(g, e, A::AbstractMatrix)
+        all(isa.(g, Kernel)) || error("`g` should be an collection of kernels")
+        all(isa.(e, Kernel)) || error("`e` should be an collection of kernels")
+        (length(e), length(g)) == size(A) || 
+            error("Size of A not compatible to the given array of kernels")
+        return new{typeof(g), typeof(e), typeof(A)}(g, e, A)
+    end
+end
+
+function (κ::LatentFactorMOKernel)((x, px)::Tuple{Vector, Int}, (y, py)::Tuple{Vector, Int})
+    if px == py
+        return sum([κ.g[i](x, y) * κ.A[px, i] for i in 1:length(κ.g)]) + 
+            κ.e[px](x, y)
+    else
+        return 0.0
+    end
+end
+
+function kernelmatrix(k::LatentFactorMOKernel, x::MOInput, y::MOInput)
+    x.out_dim == y.out_dim || error("`x` and `y` should have the same output dimension")
+    x.out_dim == size(k.A, 1) ||
+        error("Kernel not compatible with the given multi-output inputs")
+    return k.(x, permutedims(collect(y)))
+end
+
+function Base.show(io::IO, k::LatentFactorMOKernel)
+    print(io, "Semi-parametric Latent Factor Multi-Output Kernel")
+end
+
+function Base.show(io::IO, ::MIME"text/plain", k::LatentFactorMOKernel)
+    print(
+        io, 
+        "Semi-parametric Latent Factor Multi-Output Kernel\n\tgᵢ: ", 
+        [string(gi, "\n\t\t") for gi in k.g]...,
+        "\n\teᵢ: ",
+        [string(ei, "\n\t\t") for ei in k.e]...,
+    )    
+end

test/mokernels/independent.jl

@@ -1,14 +1,14 @@
 @testset "independent" begin
-    x = MOInput([rand(5) for _ in 1:4], 3)
-    y = MOInput([rand(5) for _ in 1:4], 3)
+    x1 = MOInput([rand(5) for _ in 1:4], 3)
+    x2 = MOInput([rand(5) for _ in 1:4], 3)
 
     k = IndependentMOKernel(GaussianKernel())
     @test k isa IndependentMOKernel
     @test k isa Kernel
     @test k.kernel isa KernelFunctions.BaseKernel
-    @test k(x[2], y[2]) isa Real
+    @test k(x1[2], x2[2]) isa Real
 
-    @test kernelmatrix(k, x, y) == kernelmatrix(k, collect(x), collect(y))
-    @test kernelmatrix(k, x, x) == kernelmatrix(k, x)
+    @test kernelmatrix(k, x1, x2) == kernelmatrix(k, collect(x1), collect(x2))
+    @test kernelmatrix(k, x1, x1) == kernelmatrix(k, x1)
     @test string(k) == "Independent Multi-Output Kernel\n\tSquared Exponential Kernel"
 end

test/mokernels/slfm.jl

@@ -0,0 +1,17 @@
+@testset "slfm" begin
+    x1 = MOInput([rand(5) for _ in 1:4], 2)
+    x2 = MOInput([rand(5) for _ in 1:4], 2)
+
+    k = LatentFactorMOKernel(
+        [MaternKernel(), SqExponentialKernel(), FBMKernel()],
+        [ExponentialKernel(), PeriodicKernel(5)],
+        rand(2, 3)
+    )
+    @test k isa LatentFactorMOKernel
+    @test k isa Kernel
+    @test k(x1[2], x2[2]) isa Real
+
+    @test kernelmatrix(k, x1, x2) == kernelmatrix(k, collect(x1), collect(x2))
+    @test kernelmatrix(k, x1, x1) == kernelmatrix(k, x1)
+
+end

test/runtests.jl

@@ -108,6 +108,7 @@ using KernelFunctions: metric, kappa, ColVecs, RowVecs
     @testset "multi_output" begin
         include(joinpath("mokernels", "moinput.jl"))
         include(joinpath("mokernels", "independent.jl"))
+        include(joinpath("mokernels", "slfm.jl"))
     end
     @info "Ran tests on Multi-Output Kernels"