Bayesian Gaussian mixture with variational inference (VBGMM)

Mean-field VB with Dirichlet(alpha0) prior on mixing weights; responsibility uses E[log pi_k] = psi(alpha_k) - psi(sum alpha) via morie_geron_digamma, which prunes unneeded components as alpha0 -> 0.

Usage

morie_geron_variational_bayes_gmm(
  X,
  n_components = 3,
  max_iter = 100,
  alpha0 = 0.01,
  tol = 1e-06,
  var_floor = 1e-06,
  seed = 0
)

Arguments

X

Data (n, d).

n_components, max_iter, alpha0, tol, var_floor, seed

As in Python original.

Value

list with weights, means, variances, resp, labels, alpha, n_effective, n_iter, estimate, n, method.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_geron_variational_bayes_gmm(V)
#> $weights
#> [1] 0.1256918 0.7486163 0.1256918
#> 
#> $means
#>      [,1]
#> [1,]  1.0
#> [2,]  4.5
#> [3,]  8.0
#> 
#> $variances
#>          [,1]
#> [1,] 0.000001
#> [2,] 2.918827
#> [3,] 0.000001
#> 
#> $resp
#>           [,1]         [,2]      [,3]
#> [1,] 0.9993055 0.0006945169 0.0000000
#> [2,] 0.0000000 1.0000000000 0.0000000
#> [3,] 0.0000000 1.0000000000 0.0000000
#> [4,] 0.0000000 1.0000000000 0.0000000
#> [5,] 0.0000000 1.0000000000 0.0000000
#> [6,] 0.0000000 1.0000000000 0.0000000
#> [7,] 0.0000000 1.0000000000 0.0000000
#> [8,] 0.0000000 0.0006945169 0.9993055
#> 
#> $labels
#> [1] 0 1 1 1 1 1 1 2
#> 
#> $alpha
#> [1] 1.009305 6.011389 1.009305
#> 
#> $n_effective
#> [1] 3
#> 
#> $n_iter
#> [1] 35
#> 
#> $estimate
#> [1] 3
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Mean-field VB with a Dirichlet prior on the weights (E[log pi] via digamma) and MAP diagonal Gaussians"
#>