PPCA

Julia package for Probabilistic Principal Components Analysis as described in "Variational Principal Components Analysis".

Usage

You first need to create a PPCAModel:

julia> model = PPCAModel(datadim = 2, latentdim = 2)
PPCAModelHP{Float64,2,2}:
  αprior:
    ExpFamilyDistributions.Gamma{Float64}:
      α = 0.001
      β = 0.001
  wprior:
    ExpFamilyDistributions.Normal{Float64,3}:
      μ = [0.0, 0.0, 0.0]
      Σ = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0]
  hprior:
    ExpFamilyDistributions.Normal{Float64,2}:
      μ = [0.0, 0.0]
      Σ = [1.0 0.0; 0.0 1.0]
  λprior:
    ExpFamilyDistributions.Gamma{Float64}:
      α = 0.001
      β = 0.001

In practice, you should set latentdim between 1 and datadim - 1 (included). If you set, as in the example above, latentdim greater or equal to datadim, the model will automatically shrink the extra bases to zero during training (see illustration).

Then, you need to initialize the variational posteriors. This is easily done by:

julia> θposts = θposteriors(model)
Dict{Symbol,Any} with 3 entries:
  :α => ExpFamilyDistributions.Gamma{Float64}[Gamma{Float64}:…
  :w => ExpFamilyDistributions.Normal{Float64,2}[Normal{Float64,2}:…
  :λ => Gamma{Float64}:…

For training, you need to provide a data loader from the BasicDataLoaders package to access the data, and simply call fit!:

julia> dl = ... # Data loader
julia> fit!(model, dl, θposts, epochs = 10)

The training will be run in parallel if there are several workers available. To add workers, see addprocs.

Finally, to extract the latent posteriors:

julia> X = dl[1] # Use the 1st batch of the data loader
julia> hposteriors(model, X, θposts)
10-element Array{Normal{Float64,2},1}:
 Normal{Float64,2}:
  μ = [1.7512436452299205, -9.956494453759758e-8]
  Σ = [0.028248509216655084 5.1464934731583015e-8; 5.1464934731583015e-8 0.9657413079963144]
 Normal{Float64,2}:
  μ = [-1.7016493202424885, 9.674530645698072e-8]
  Σ = [0.028248509216655084 5.1464934731583015e-8; 5.1464934731583015e-8 0.9657413079963144]
...

For a complete example, have a look at the example jupyter notebook.