[Question] Train a multi-input multi-output model with corregionalization.

[david-vicente]

I managed to train a multi-input single-output with no issues. Consider the fake data:

x1 = -5:0.8:5
x2 = -5:0.8:5

xx1 = vec([i for i in x1, j in x2])
xx2 = vec([j for i in x1, j in x2])

X = [x1 x2]

h(x, y) = 10 * (sin(x^2 + y^2) / (x^2 + y^2)) + 10
Y = [h(i,j) for (i,j) in zip(xx1, xx2)];

i simply used this model

kernel = KernelFunctions.SqExponentialKernel()
m = GP(X, Y, kernel,opt_noise=false)

Now imagine that I want to a multi-output setting, such that my data is now

x1 = -5:0.8:5
x2 = -5:0.8:5

xx1 = vec([i for i in x1, j in x2])
xx2 = vec([j for i in x1, j in x2])

X = [x1 x2]

h(x, y) = 10 * (sin(x^2 + y^2) / (x^2 + y^2)) + 10
g(x, y) = -1 / (x^2 + y^2 + 1) + 10


y1 = [h(i,j) for (i,j) in zip(xx1, xx2)];
y2 = [g(i,j) for (i,j) in zip(xx1, xx2)];

Y = [y1 y2]

How should I proceed? There aren't any examples for this case in the docs.

[david-vicente]

I also noticed that the signatures of the constructors for MOARGP, MOSVGP an MOVGP require that the input labels variable y is a AbstractVector{<:AbstractArray}, so we can't pass a Matrix.

[theogf]

Hi, you're right, there's unfortunately no example for multiple output.
Given your provided example you can do
MOVGP(X, [y1, y2], kernel, Gaussian Likelihood(), AnalyticVI(), 2)
If you want to have an analytic solution I would however recommend you having a look at JuliaGaussianProcesses/AbstractGPs.jl#30

[david-vicente]

Trying your suggestion gives me:

BoundsError: attempt to access 1-element Array{Int64,1} at index [2]

Stacktrace:
 [1] getindex at ./array.jl:809 [inlined]
 [2] #76 at /home/myuser/.julia/packages/AugmentedGaussianProcesses/93OMX/src/inference/analyticVI.jl:49 [inlined]
 [3] ntuple(::AugmentedGaussianProcesses.var"#76#77"{Float64,Array{Int64,1},Descent}, ::Int64) at ./ntuple.jl:18
 [4] AnalyticVI{Float64,1}(::Float64, ::Bool, ::Array{Int64,1}, ::Array{Int64,1}, ::Array{Int64,1}, ::Int64, ::Descent) at /home/myuser/.julia/packages/AugmentedGaussianProcesses/93OMX/src/inference/analyticVI.jl:49
 [5] tuple_inference(::AnalyticVI{Float64,1}, ::Int64, ::Array{Int64,1}, ::Array{Int64,1}, ::Array{Int64,1}) at /home/myuser/.julia/packages/AugmentedGaussianProcesses/93OMX/src/inference/analyticVI.jl:106
 [6] MOVGP(::Array{Float64,2}, ::Array{Array{Float64,1},1}, ::SqExponentialKernel, ::GaussianLikelihood{Float64,Nothing,Array{Float64,1}}, ::AnalyticVI{Float64,1}, ::Int64; verbose::Int64, optimiser::ADAM, atfrequency::Int64, mean::ZeroMean{Float64}, variance::Float64, Aoptimiser::ADAM, ArrayType::UnionAll) at /home/myuser/.julia/packages/AugmentedGaussianProcesses/93OMX/src/models/MOVGP.jl:147
 [7] MOVGP(::Array{Float64,2}, ::Array{Array{Float64,1},1}, ::SqExponentialKernel, ::GaussianLikelihood{Float64,Nothing,Array{Float64,1}}, ::AnalyticVI{Float64,1}, ::Int64) at /home/myuser/.julia/packages/AugmentedGaussianProcesses/93OMX/src/models/MOVGP.jl:76
 [8] top-level scope at In[9]:4