predict_gmm {mtlgmm}

Clustering new observations based on fitted GMM estimators.

Description

Clustering new observations based on fitted GMM estimators, which is an empirical version of Bayes classifier. See equation (13) in Tian, Y., Weng, H., & Feng, Y. (2022).

Usage

predict_gmm(w, mu1, mu2, beta, newx)

Arguments

w

the estimate of mixture proportion in the GMM. Numeric.

mu1

the estimate of Gaussian mean of the first cluster in the GMM. Should be a vector.

mu2

the estimate of Gaussian mean of the first cluster in the GMM. Should be a vector.

beta

the estimate of the discriminant coefficient for the GMM. Should be a vector.

newx

design matrix of new observations. Should be a matrix.

Value

A vector of predicted labels of new observations.

References

Tian, Y., Weng, H., & Feng, Y. (2022). Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models. arXiv preprint arXiv:2209.15224.

See Also

mtlgmm, tlgmm, data_generation, initialize, alignment, alignment_swap, estimation_error, misclustering_error.

Examples

set.seed(23, kind = "L'Ecuyer-CMRG")
## Consider a 5-task multi-task learning problem in the setting "MTL-1"
data_list <- data_generation(K = 5, outlier_K = 1, simulation_no = "MTL-1", h_w = 0.1,
h_mu = 1, n = 50)  # generate the data
x_train <- sapply(1:length(data_list$data$x), function(k){
  data_list$data$x[[k]][1:50,]
}, simplify = FALSE)
x_test <- sapply(1:length(data_list$data$x), function(k){
  data_list$data$x[[k]][-(1:50),]
}, simplify = FALSE)
y_test <- sapply(1:length(data_list$data$x), function(k){
  data_list$data$y[[k]][-(1:50)]
}, simplify = FALSE)

fit <- mtlgmm(x = x_train, C1_w = 0.05, C1_mu = 0.2, C1_beta = 0.2,
C2_w = 0.05, C2_mu = 0.2, C2_beta = 0.2, kappa = 1/3, initial_method = "EM",
trim = 0.1, lambda_choice = "fixed", step_size = "lipschitz")

y_pred <- sapply(1:length(data_list$data$x), function(i){
predict_gmm(w = fit$w[i], mu1 = fit$mu1[, i], mu2 = fit$mu2[, i],
beta = fit$beta[, i], newx = x_test[[i]])
}, simplify = FALSE)
misclustering_error(y_pred[-data_list$data$outlier_index],
y_test[-data_list$data$outlier_index], type = "max")