An S4 class to represent a multivariate Gaussian mixture model, extend icl_model-class. The model corresponds to the following generative model: $$\pi \sim Dirichlet(\alpha)$$ $$Z_i \sim \mathcal{M}(1,\pi)$$ $$V_k \sim \mathcal{W}(\varepsilon^{-1},n_0)$$ $$\mu_k \sim \mathcal{N}(\mu,(\tau V_k)^{-1})$$ $$X_{i}|Z_{ik}=1 \sim \mathcal{N}(\mu_k,V_{k}^{-1})$$ with $$\mathcal{W}(\varepsilon^{-1},n_0)$$ the Whishart distribution.

## Slots

name

name of the model

alpha

Dirichlet over cluster proportions prior parameter (default to 1)

tau

Prior parameter (inverse variance) default 0.01

N0

Prior parameter (pseudo count) should be > number of features (default to NaN, in this case it will be estimated from data as the number of columns of X)

epsilon

Prior parameter co-variance matrix prior (matrix of size D x D), (default to a matrix of NaN, in this case epsilon will be estimated from data and will corresponds to 0.1 times a diagonal matrix with the variances of the X columns)

mu

Prior parameters for the means (vector of size D), (default to NaN, in this case mu will be estimated from the data and will be equal to the mean of X)

## References

Bertoletti, Marco & Friel, Nial & Rastelli, Riccardo. (2014). Choosing the number of clusters in a finite mixture model using an exact Integrated Completed Likelihood criterion. METRON. 73. 10.1007/s40300-015-0064-5. #'

## Examples

new("gmm")
#> An object of class "gmm"
#> Slot "tau":
#> [1] 0.001
#>
#> Slot "mu":
#> [1] NaN
#>
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#>
#> Slot "N0":
#> [1] NaN
#>
#> Slot "name":
#> [1] "gmm"
#>
#> Slot "alpha":
#> [1] 1
#> new("gmm",alpha=1,tau=0.1,N0=15)
#> An object of class "gmm"
#> Slot "tau":
#> [1] 0.1
#>
#> Slot "mu":
#> [1] NaN
#>
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#>
#> Slot "N0":
#> [1] 15
#>
#> Slot "name":
#> [1] "gmm"
#>
#> Slot "alpha":
#> [1] 1
#>