Zygote.gradient does not work with AbstractGPs.CustomMean

General Usage
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1

Hello, I am trying to use an AbstractGPs.FiniteGP with Turing and I am having problems with Zygote.gradient calculation of the GP hyperparameters.

For some reason, Zygote fails to calculate the gradient when using an AbstractGPs.CustomMean but works properly when using AbstractGPs.ZeroMean.

When I try using ForwardDiff instead, both gradients are calculated without an issue.

MWE of the issue:

using AbstractGPs
using Zygote
using ForwardDiff

X = [1.; 2.; 3.;;]
y = [1., 2., 3.]

function construct_finite_gp(X, lengthscale, noise; min_param_val=1e-6, mean)
    # for numerical stability
    lengthscale = lengthscale + min_param_val
    noise = noise + min_param_val

    kernel = with_lengthscale(Matern52Kernel(), lengthscale)
    return GP(mean, kernel)(X', noise)
end

function f(noise; mean)
    gp = construct_finite_gp(X, 1., first(noise); mean)
    return logpdf(gp, y)
end

forwarddiff_zeromean = ForwardDiff.gradient(n -> f(n; mean=AbstractGPs.ZeroMean()), [1.])
@show forwarddiff_zeromean

forwarddiff_custommean = ForwardDiff.gradient(n -> f(n; mean=AbstractGPs.CustomMean(x->0.)), [1.])
@show forwarddiff_custommean

zygote_zeromean = Zygote.gradient(n -> f(n; mean=AbstractGPs.ZeroMean()), 1.)
@show zygote_zeromean

zygote_custommean = Zygote.gradient(n -> f(n; mean=AbstractGPs.CustomMean(x->0.)), 1.)
@show zygote_custommean

The result of running the MWE:

forwarddiff_zeromean = [0.2630913490608584]
forwarddiff_custommean = [0.2630913490608584]
zygote_zeromean = (0.26309134906085807,)
ERROR: MethodError: no method matching +(::NamedTuple{(:X,), Tuple{Matrix{Float64}}}, ::Vector{Nothing})
Closest candidates are:
  +(::Any, ::Any, ::Any, ::Any...) at operators.jl:591
  +(::Distributions.MvNormal, ::AbstractVector) at C:\Users\sheld\.julia\packages\Distributions\7iOJp\src\multivariate\mvnormal.jl:294
  +(::SparseArrays.AbstractSparseMatrixCSC, ::Array) at C:\Users\sheld\AppData\Local\Programs\Julia-1.8.0\share\julia\stdlib\v1.8\SparseArrays\src\sparsematrix.jl:1832
  ...
Stacktrace:
  [1] accum(x::NamedTuple{(:X,), Tuple{Matrix{Float64}}}, y::Vector{Nothing}) (repeats 2 times)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\lib\lib.jl:17
  [2] (::typeof(∂(mean_and_cov)))(Δ::Tuple{Vector{Float64}, LinearAlgebra.UpperTriangular{Float64, Matrix{Float64}}})    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
  [3] Pullback
    @ C:\Users\sheld\.julia\packages\AbstractGPs\e2ey8\src\finite_gp_projection.jl:134 [inlined]
  [4] (::typeof(∂(mean_and_cov)))(Δ::Tuple{Vector{Float64}, LinearAlgebra.UpperTriangular{Float64, Matrix{Float64}}})    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
  [5] Pullback
    @ C:\Users\sheld\.julia\packages\AbstractGPs\e2ey8\src\finite_gp_projection.jl:307 [inlined]
  [6] (::typeof(∂(logpdf)))(Δ::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
  [7] Pullback
    @ d:\plzen\sandbox\sampling_error_mwe\zygote_mwe.jl:19 [inlined]
  [8] (::typeof(∂(#f#47)))(Δ::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
  [9] Pullback
    @ d:\plzen\sandbox\sampling_error_mwe\zygote_mwe.jl:17 [inlined]
 [10] (::typeof(∂(f##kw)))(Δ::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
 [11] Pullback
    @ d:\plzen\sandbox\sampling_error_mwe\zygote_mwe.jl:31 [inlined]
 [12] (::typeof(∂(#56)))(Δ::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface2.jl:0
 [13] (::Zygote.var"#60#61"{typeof(∂(#56))})(Δ::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface.jl:45
 [14] gradient(f::Function, args::Float64)
    @ Zygote C:\Users\sheld\.julia\packages\Zygote\dABKa\src\compiler\interface.jl:97
 [15] top-level scope
    @ d:\plzen\sandbox\sampling_error_mwe\zygote_mwe.jl:31

I need to use Zygote because of this issue.

Does anyone know what might be the cause of this?
Is it a bug in Zygote or AbstractGPs or some error on my side?

2

Hi @soldasim . This sounds like a frustrating issue.

Would I be correct in assuming that you’re not actually interested in using the custom mean function CustomMean(x -> 0.)? Would you mind providing the one that you’re actually interested in?

3

Hi @willtebbutt,

in my model I am using a parametric model as the mean of the GP.
I want the code to be general, so the parametric model is to be defined by the user, so I need it to work with any real function.

An example could be:

function param_model(x, params)
    return params[1] * cos(params[2] * x[1]) + params[3]
end

zygote_custommean = Zygote.gradient(n -> f(n; mean=AbstractGPs.CustomMean(x -> param_model(x, [1.,2.,3.]))), 1.)

EDIT: error in the example

4

Okay, thanks for the additional info.

One more question: is the actual value of X that you plan to use going to be multi-dimensional, or do you only ever do 1D stuff?

5

X can be multidimensional.

6

Great.

In that case I would suggest implementing a new mean function, so that you can implement _map_meanfunction for it, and get the appropriate cotangent type when you work with ColVecs and RowVecs.

In particular, I would do something like

struct ParamModel{Tparams} <: AbstractGPs.MeanFunction
    params::Tparams
end

function AbstractGPs._map_meanfunction(m::ParamModel, x::ColVecs)
    X = x.X
    # whatever computation needs to happen on `X` using broadcasting etc
end


function AbstractGPs._map_meanfunction(m::ParamModel, x::RowVecs)
    X = x.X
    # whatever computation needs to happen on `X` using broadcasting etc
end

What’s gong wrong with AD at the minute is that the ChainRulesCore.rrule for map doesn’t do the right thing for ColVecs and RowVecs, which is what _map_meanfunction hits for CustomMean. By implementing _map_meanfunction on your own type, you can ensure that you never hit this code path.

It’s an annoying work-around to have to make, but that’s (unfortunately) where we are with AD at the minute.

2 Likes
7

Thank you so much! It would have been difficult for me to find the cause as I’m not that experienced in julia yet.

I’ve generalized the solution into

struct MyCustomMean{Tf} <: AbstractGPs.MeanFunction
    f::Tf
end

function AbstractGPs._map_meanfunction(m::MyCustomMean, x::ColVecs)
    X = x.X
    map(m.f, eachcol(X))
end

function AbstractGPs._map_meanfunction(m::MyCustomMean, x::RowVecs)
    X = x.X
    map(m.f, eachcol(X))
end

so that MyCustomMean can be used exactly like AbstractGPs.CustomMean.

The code seems to work now:

julia> ForwardDiff.gradient(n -> f(n; mean=AbstractGPs.CustomMean(x->0.)), [1.])
1-element Vector{Float64}:
 0.2630913490608584

julia> ForwardDiff.gradient(n -> f(n; mean=MyCustomMean(x->0.)), [1.])
1-element Vector{Float64}:
 0.2630913490608584

julia> Zygote.gradient(n -> f(n; mean=MyCustomMean(x->0.)), 1.)
(0.26309134906085807,)

Thank you for your time and help :slight_smile:

1 Like