Re: [julia-users] Random Draw from Gaussian Mixture

[David van Leeuwen]

Hi, 

Did you look into GaussianMixtures?  This has a random sampling function. 

---david

On Friday, December 19, 2014 1:42:38 PM UTC+1, Andreas Noack wrote:
>
> Hi Bradley
>
> I was able to construct an GMM instance with
>
> julia> Σnew = 
> Triangular{Float64,Matrix{Float64},:U,false}[chol(sigma[:,:,i], :U) for i = 
> 1:2]
>
> julia> GMM(p, mu, Σnew, [], 0)
> GMM{Float64} with 2 components in 2 dimensions and full covariance
> Mix 1: weight 0.90
> mean: 1x2 Array{Float64,2}:
>  0.0  25.0
> covariance: 2x2 Array{Float64,2}:
>   5.26316  -4.73684
>  -4.73684   5.26316
> Mix 2: weight 0.10
> mean: 1x2 Array{Float64,2}:
>  0.0  25.0
> covariance: 2x2 Array{Float64,2}:
>  0.13  0.0 
>  0.0   0.13
>
> but I don't understant the last two arguments to the constructor.
>
> 2014-12-18 1:06 GMT+01:00 Bradley Setzler  >:
> >
> > Hi,
> >
> > I wish to work with the Gaussian Mixture distribution (especially rand 
> and pdf), exactly as in this example: 
> >
> > mu = [0.0 25.0; 0.0 25.0] 
> > sigma = Array(Float64, 2, 2, 2) 
> > sigma[:, :, 1] = [1.0 0.9; 0.9 1.0] 
> > sigma[:, :, 2] = 7.5 * [1.0 0.0; 0.0 1.0] 
> > p = [0.9, 0.1] 
> >
> > distr = MixtureMultivariateNormals(mu, sigma, p) 
> > X = rand(distr, 10_000)
> >
> >
> > However, the method MixtureMultivariateNormals(mu, sigma, p) used in 
> that example no longer exists. The maintained version of MixtureModels.jl 
> has no examples or methods in the documentation of basic usage, and it is 
> far from obvious how to use it for a Gaussian mixture.
> >
> > Separately, the package GaussianMixtures.jl, does not successfully work 
> in what would seem to be the obvious method:
> >
> > julia> GMM(p,mu,sigma)
> > ERROR: `GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}` has no 
> method matching 
> GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}(::Array{Float64,1}, 
> ::Array{Float64,2}, ::Array{Float64,2})
> >
> > Could someone show me a working example analogous to the one above, 
> using whichever package you wish?
> >
> > Thank you,
> > Bradley
>

Re: [julia-users] Random Draw from Gaussian Mixture

[Andreas Noack]

Hi Bradley

I was able to construct an GMM instance with

julia> Σnew =
Triangular{Float64,Matrix{Float64},:U,false}[chol(sigma[:,:,i], :U) for i =
1:2]

julia> GMM(p, mu, Σnew, [], 0)
GMM{Float64} with 2 components in 2 dimensions and full covariance
Mix 1: weight 0.90
mean: 1x2 Array{Float64,2}:
 0.0  25.0
covariance: 2x2 Array{Float64,2}:
  5.26316  -4.73684
 -4.73684   5.26316
Mix 2: weight 0.10
mean: 1x2 Array{Float64,2}:
 0.0  25.0
covariance: 2x2 Array{Float64,2}:
 0.13  0.0
 0.0   0.13

but I don't understant the last two arguments to the constructor.

2014-12-18 1:06 GMT+01:00 Bradley Setzler :
>
> Hi,
>
> I wish to work with the Gaussian Mixture distribution (especially rand
and pdf), exactly as in this example:
>
> mu = [0.0 25.0; 0.0 25.0]
> sigma = Array(Float64, 2, 2, 2)
> sigma[:, :, 1] = [1.0 0.9; 0.9 1.0]
> sigma[:, :, 2] = 7.5 * [1.0 0.0; 0.0 1.0]
> p = [0.9, 0.1]
>
> distr = MixtureMultivariateNormals(mu, sigma, p)
> X = rand(distr, 10_000)
>
>
> However, the method MixtureMultivariateNormals(mu, sigma, p) used in that
example no longer exists. The maintained version of MixtureModels.jl has no
examples or methods in the documentation of basic usage, and it is far from
obvious how to use it for a Gaussian mixture.
>
> Separately, the package GaussianMixtures.jl, does not successfully work
in what would seem to be the obvious method:
>
> julia> GMM(p,mu,sigma)
> ERROR: `GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}` has no
method matching
GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}(::Array{Float64,1},
::Array{Float64,2}, ::Array{Float64,2})
>
> Could someone show me a working example analogous to the one above, using
whichever package you wish?
>
> Thank you,
> Bradley

[julia-users] Random Draw from Gaussian Mixture

[Bradley Setzler]

Hi,

I wish to work with the Gaussian Mixture distribution (especially rand and 
pdf), exactly as in this example 
: 

mu = [0.0 25.0; 0.0 25.0] 
sigma = Array(Float64, 2, 2, 2) 
sigma[:, :, 1] = [1.0 0.9; 0.9 1.0] 
sigma[:, :, 2] = 7.5 * [1.0 0.0; 0.0 1.0] 
p = [0.9, 0.1] 

distr = MixtureMultivariateNormals(mu, sigma, p) 
X = rand(distr, 10_000)


However, the method MixtureMultivariateNormals(mu, sigma, p) used in that 
example no longer exists. The maintained version of MixtureModels.jl 
 has no examples or methods 
in the documentation of basic usage, and it is far from obvious how to use 
it for a Gaussian mixture.

Separately, the package GaussianMixtures.jl 
, does not successfully 
work in what would seem to be the obvious method:

julia> GMM(p,mu,sigma)
ERROR: `GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}` has no 
method matching 
GMM{T<:FloatingPoint,CT<:Union(Array{T,2},Array{T,1})}(::Array{Float64,1}, 
::Array{Float64,2}, ::Array{Float64,2})

Could someone show me a working example analogous to the one above, using 
whichever package you wish?

Thank you,
Bradley