Mix Gaussian mixtures into one mixture

Flattens a list of Gaussian mixtures into a single mixture whose density is the weighted average \(\sum_b \alpha_b\, g_b(x)\) – model averaging, prior pooling, or the mixture-of-mixtures construction.

Usage

gmm_mix(gmms, weights = NULL)

Arguments

gmms

A non-empty list of gmm (or gmm_fit) objects sharing one ambient dimension.

weights

Optional non-negative mixing weights, one per element of gmms (normalised internally). Default: equal weights.

Value

A gmm with sum(K_b) components.

See also

Other operators: gmm_affine(), gmm_aggregate(), gmm_convolve(), gmm_counterfactual(), gmm_filter(), gmm_intervene(), gmm_missing(), gmm_observe(), gmm_product(), gmm_reduce()

Examples

g1 <- gmm(weights = 1, means = list(-1), covariances = list(matrix(1)))
g2 <- gmm(weights = 1, means = list(2), covariances = list(matrix(0.5)))
gmm_mix(list(g1, g2), weights = c(0.7, 0.3))
#> <mix[2]>: K = 2 components in p = 1 dimensions
#>   [1] w = 0.7000, |mu| = 1.0000, tr(Sigma) = 1.0000
#>   [2] w = 0.3000, |mu| = 2.0000, tr(Sigma) = 0.5000