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Sampling from von Mises Fisher yields NaN #1423

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lanceXwq opened this issue Nov 15, 2021 · 2 comments · May be fixed by #1930
Open

Sampling from von Mises Fisher yields NaN #1423

lanceXwq opened this issue Nov 15, 2021 · 2 comments · May be fixed by #1930

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@lanceXwq
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This happens when the mean direction unit vector μ is along the x-axis. For instance:

julia> vMF = VonMisesFisher([1, 0], 1.0)
VonMisesFisher{Float64}(μ=[1.0, 0.0], κ=1.0)
julia> rand(vMF)
2-element Vector{Float64}:
 NaN
 NaN

This problem seems to persist in higher dimensions.
@devmotion
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I'm not familiar with the implementation of the VonMisesFisher sampler but I suspect that the NaNs arise in

Distributions.jl/src/samplers/vonmisesfisher.jl

Line 103 in 8887d7a

v[1] /= s
: for μ=[1.0, 0.0] we have v[1] = s = 0 in this line, and hence v[1] /= s should result in v[1] = NaN.

@devmotion devmotion mentioned this issue Dec 27, 2021
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@trahflow
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I just stumbled over this as well.

I'm not familiar with the implementation of the VonMisesFisher sampler but I suspect that the NaNs arise in

Distributions.jl/src/samplers/vonmisesfisher.jl

Line 103 in 8887d7a

v[1] /= s

: for μ=[1.0, 0.0] we have v[1] = s = 0 in this line, and hence v[1] /= s should result in v[1] = NaN.

Yes, this is what happens.
It seems this was introduced in #1162. At least a quick check shows the previous version which constructs an explicit rotation matrix does not suffer from this.

A very quick, albeit a bit dirty fix would be to return a zero vector in

Distributions.jl/src/samplers/vonmisesfisher.jl

Lines 87 to 102 in 13029c0

function _vmf_householder_vec(μ::Vector{Float64})
# assuming μ is a unit-vector (which it should be)
# can compute v in a single pass over μ
p = length(μ)
v = similar(μ)
v[1] = μ[1] - 1.0
s = sqrt(-2*v[1])
v[1] /= s
@inbounds for i in 2:p
v[i] = μ[i] / s
end
return v
end

for the case that s is numerically close to zero. That should give the correct (identity) rotation in

Distributions.jl/src/samplers/vonmisesfisher.jl

Line 46 in 13029c0

return _vmf_rot!(spl.v, x)

Maybe @emerali has a suggestion?

@williamjsdavis williamjsdavis mentioned this issue Nov 20, 2024
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@devmotion devmotion linked a pull request Dec 16, 2024 that will close this issue
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Fix von Mises-Fisher sampler JuliaStats/Distributions.jl
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@devmotion @trahflow @lanceXwq