JuliaGaussianProcesses / JuliaGaussianProcesses/AbstractGPs.jl

PosDef error for RBF kernel

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Description

Hello, I am not sure if this is just on my machine, but I can't seem to sample from prior RBF GPs or posteriors trained on them. For instance, something as simple as

x = range(0,5,30)
f = GP(SEKernel())
plot(rand(f(x), 10))

results in the error

PosDefException: matrix is not positive definite; Cholesky factorization failed.

Stacktrace:
 [1] checkpositivedefinite
   @ ~/.julia/juliaup/julia-1.10.2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/factorization.jl:67 [inlined]
 [2] cholesky!(A::Symmetric{Float64, Matrix{Float64}}, ::NoPivot; check::Bool)
   @ LinearAlgebra ~/.julia/juliaup/julia-1.10.2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/cholesky.jl:269
 [3] cholesky! (repeats 2 times)
   @ ~/.julia/juliaup/julia-1.10.2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/cholesky.jl:267 [inlined]
 [4] cholesky(A::Symmetric{Float64, Matrix{Float64}}, ::NoPivot; check::Bool)
   @ LinearAlgebra ~/.julia/juliaup/julia-1.10.2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/cholesky.jl:401
 [5] cholesky (repeats 2 times)
   @ ~/.julia/juliaup/julia-1.10.2+0.aarch64.apple.darwin14/share/julia/stdlib/v1.10/LinearAlgebra/src/cholesky.jl:401 [inlined]
 [6] rand(rng::Random._GLOBAL_RNG, f::AbstractGPs.FiniteGP{GP{ZeroMean{Float64}, SqExponentialKernel{Distances.Euclidean}}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, Diagonal{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}}}, N::Int64)
   @ AbstractGPs ~/.julia/packages/AbstractGPs/IOYUf/src/finite_gp_projection.jl:235
 [7] rand(f::AbstractGPs.FiniteGP{GP{ZeroMean{Float64}, SqExponentialKernel{Distances.Euclidean}}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, Diagonal{Float64, FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}}}}, N::Int64)
   @ AbstractGPs ~/.julia/packages/AbstractGPs/IOYUf/src/finite_gp_projection.jl:238
 [8] top-level scope
   @ In[128]:3

Unless I change the input sample size to something small like range(0,5,20).

Other kernels, e.g.,

x = range(0,5,30)
f = GP(Matern32Kernel())
plot(rand(f(x), 10))

run without any issue. Thank you in advance for your help.

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  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Reproduce the RBF example with range(0,5,30) and compare it with the working 20-point case and Matern32 example. Start at AbstractGPs/src/finite_gp_projection.jl:235, where rand performs the failing Cholesky factorization, and inspect the generated covariance matrix. Done means sampling succeeds for the reported 30-point RBF input without the PosDefException.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
machine-learning
Issue type
Bug
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
42/100

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