DiagGmm function

Diagonal Gaussian Mixture Model Prior description class

An S4 class to represent a multivariate diagonal Gaussian mixture model. The model corresponds to the following generative model: [REMOVE_ME]$\pi \sim Dirichlet(\alpha) [REMOVE_ME_2]$

[REMOVE_ME]$Z_i \sim \mathcal{M}(1,\pi) [REMOVE_ME_2]$

[REMOVE_ME]$\lambda_k^{(d)} \sim \mathcal{G}(\kappa,\beta) [REMOVE_ME_2]$

[REMOVE_ME]$\mu_k^{(d)} \sim \mathcal{N}(\mu,(\tau \lambda_k)^{-1}) [REMOVE_ME_2]$

[REMOVE_ME]$X_{i.}|Z_{ik}=1 \sim \mathcal{N}(\mu_k,\lambda_{k}^{-1}) [REMOVE_ME_2]$

with $\mathcal{G}(\kappa,\beta)$ the Gamma distribution with shape parameter $\kappa$ and rate parameter $\beta$. These classes mainly store the prior parameters value ($\alpha,\tau,\kappa\beta,\mu$) of this generative model. The DiagGmm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DiagGmmPrior-class must be sued when fitting a CombinedModels-class. class

DiagGmmPrior(tau = 0.01, kappa = 1, beta = NaN, mu = NaN)

DiagGmm(alpha = 1, tau = 0.01, kappa = 1, beta = NaN, mu = NaN)

Arguments

• tau: Prior parameter (inverse variance), (default 0.01)
• kappa: Prior parameter (gamma shape), (default to 1)
• beta: Prior parameter (gamma rate), (default to NaN, in this case beta will be estimated from data as 0.1 time the mean of X columns variances)
• mu: Prior for the means (vector of size D), (default to NaN, in this case mu will be estimated from data as the mean of X)
• alpha: Dirichlet prior parameter over the cluster proportions (default to 1)

Returns

a DiagGmmPrior-class object

a DiagGmm-class object

Description

An S4 class to represent a multivariate diagonal Gaussian mixture model. The model corresponds to the following generative model:

$$\pi \sim Dirichlet(\alpha)$$ $$Z_i \sim \mathcal{M}(1,\pi)$$ $$\lambda_k^{(d)} \sim \mathcal{G}(\kappa,\beta)$$ $$\mu_k^{(d)} \sim \mathcal{N}(\mu,(\tau \lambda_k)^{-1})$$ $$X_{i.}|Z_{ik}=1 \sim \mathcal{N}(\mu_k,\lambda_{k}^{-1})$$

with $\mathcal{G}(\kappa,\beta)$ the Gamma distribution with shape parameter $\kappa$ and rate parameter $\beta$. These classes mainly store the prior parameters value ($\alpha,\tau,\kappa\beta,\mu$) of this generative model. The DiagGmm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DiagGmmPrior-class must be sued when fitting a CombinedModels-class.

Examples

DiagGmmPrior()
DiagGmmPrior(tau = 0.1)
DiagGmm()
DiagGmm(tau = 0.1)

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. #'

See Also

DiagGmmFit-class, DiagGmmPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()