Mean function

[trappmartin]

Hi, I just played around with this.. it's awesome!

Some remarks / bugs:

1. When calling mean(f) on a GP object, I get an error message in the lines of:

MethodError: no method matching iterate(::AbstractGPs.PosteriorGP{AbstractGPs.GP{AbstractGPs.ZeroMean{Float64},KernelFunctions.Matern32Kernel},NamedTuple{(:α, :C, :x, :δ),Tuple{Array{Float64,1},LinearAlgebra.Cholesky{Float64,Array{Float64,2}},KernelFunctions.ColVecs{Float64,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},SubArray{Float64,1,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},false}},Array{Float64,1}}}})
mean(::typeof(identity), ::AbstractGPs.PosteriorGP{AbstractGPs.GP{AbstractGPs.ZeroMean{Float64},KernelFunctions.Matern32Kernel},NamedTuple{(:α, :C, :x, :δ),Tuple{Array{Float64,1},LinearAlgebra.Cholesky{Float64,Array{Float64,2}},KernelFunctions.ColVecs{Float64,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},SubArray{Float64,1,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},false}},Array{Float64,1}}}})@Statistics.jl:62
mean(::AbstractGPs.PosteriorGP{AbstractGPs.GP{AbstractGPs.ZeroMean{Float64},KernelFunctions.Matern32Kernel},NamedTuple{(:α, :C, :x, :δ),Tuple{Array{Float64,1},LinearAlgebra.Cholesky{Float64,Array{Float64,2}},KernelFunctions.ColVecs{Float64,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},SubArray{Float64,1,LinearAlgebra.Adjoint{Float64,Array{Float64,2}},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},false}},Array{Float64,1}}}})@Statistics.jl:44
top-level scope@Local: 1[inlined]

2. When calling mean(f, x) on a GP object for some x, then x has to be a vector. If the covariate space is multidimensional this has to be a vector of vectors. This should be written down somewhere as I didn't know how to use mean(f, x) on a GP on a multidimensional covariate space. Maybe it is, and I didn't see it? Anyways, maybe this function could also support Arrays?

[willtebbutt]

👋

When calling mean(f) on a GP object, I get an error message in the lines of:

Hmmm yeah, I guess you wanted the mean function instead?

When calling mean(f, x) on a GP object for some x, then x has to be a vector. If the covariate space is multidimensional this has to be a vector of vectors. This should be written down somewhere as I didn't know how to use mean(f, x) on a GP on a multidimensional covariate space. Maybe it is, and I didn't see it? Anyways, maybe this function could also support Arrays?

Yeah, this is a convention that we've broadly adopted. You should wrap a matrix of inputs either in a ColVecs (if each column of said matrix corresponds to an input) or a RowVecs (if each row corresponds to a single input). Semantically these containers represent a vector-of-vectors, they just do stuff more efficiently under the hood than literally constructing a vector-of-vectors.

I agree that this needs to be documented somewhere. A PR would be very welcome :)

edit: when you say "support arrays", do you just mean matrices, or higher-dimensional things as well?

[theogf]

I think that mean(f::PosteriorGP) should automatically return the mean of the posterior distribution on the training data no (same with cov).

Also we should probably support mean(f, X::AbstractMatrix) in the same way that we support gp(X::AbstractMatrix)

[willtebbutt]

I think that mean(f::PosteriorGP) should automatically return the mean of the posterior distribution on the training data no (same with cov).

I disagree with this. A PosteriorGP is just another GP -- it typically represents some infinite-dimensional thing, so it would be weird to support this functionality. I could get on board with adding additional functions such as mean_at_training_data and cov_at_training_data though.

[willtebbutt]

I would have no problem with mean(f::PosteriorGP) returning a function that can compute the posterior mean at new locations -- it just feels a bit redundant because you can write mean(f_post(x)) instead.

[trappmartin]

Yeah, I think it's mostly an issue of documentation tbh. I don't think it makes much sense to add functionality.

[trappmartin]

But having a mean(f, X::AbstractMatrix) would make a lot of sense as you seem to be able to use X as a matrix on all other places too.

[willtebbutt]

Do we know if anyone is likely to have time work on docs any time soon? I'm completely swamped with PhD stuff at the minute.

[trappmartin]

edit: when you say "support arrays", do you just mean matrices, or higher-dimensional things as well?

Whatever makes sense. I'd say matrices, but maybe there are use-cases that would require higher-dimensional things? Dunno.

[trappmartin]

Sorry. Wrong button...

[willtebbutt]

Happens to me all the time

[theogf]

Actually @st-- proposed to help by working on some tutorials with AbstractGPs...