Remove UnivariateGMM

[simonbyrne]

I think it is completely unnecessary. It could just be implemented as an alias of MixtureModel.

If the aim is to support storing it as vectors of means and stds, it would be better doing it via StructArrays.jl.

[simonbyrne]

(also, I apologise for opening this issue the day #615 was merged)

[luiarthur]

Hi,

Not sure if this is enough motivation to keep UnivariateGMM, but here's a little benchmark that seems to show that logpdf on UnivariateGMM is much more efficient than logpdf on MixtureModel of Normals.

using Distributions
using StatsFuns
using BenchmarkTools
using Random

# Function to simulate some data for GMM logpdf.
function gendata(nobs, nmix)
  x = randn(nobs)
  mu = collect(range(-3, 3, length=nmix))
  sig = rand(nmix)
  w = let
    _w = rand(nmix)
    _w / sum(_w)
  end
  return mu, sig, w, x
end

# Shorthand for GMM logpdf
gmm_lpdf(mu, sig, w, x; dims) = sum(logsumexp(normlogpdf.(mu, sig, x) .+ log.(w), dims=dims))

# Generate data.
Random.seed!(0);
mu, sig, w, x  = gendata(100, 5)

### Benchmark ###

@btime gmm_lpdf(mu', sig', w',  x[:, :], dims=2)  # V1: 15.5 μs

@btime sum(logsumexp(logpdf.(Normal.(mu', sig'), x[:,:]) .+ log.(w'), dims=2))  # V2: 20.6μs

@btime sum(logpdf.(UnivariateGMM(mu, sig, Categorical(w)), x))  # V3: 20.9 μs

@btime sum(logpdf.(MixtureModel(Normal.(mu, sig), w), x))  # V4: 317.2 μs

I've timed 4 things that do the same thing here -- compute the sum of the log density of a location-scale mixture of Normals evaluated at a vector of 100 univariate values.

The UnivariateGMM version (V3) is over 10x faster than the MixtureModel one (V4) in this example.

These are all vectorized, so there's definitely a way to optimize further here. But I just want to illustrate the utility of having UnivariateGMM.